The Geometry of a Black Hole

Gravity is said to be the curvature of space and time, but what does such curvature actually look like? In this video we explore the foremost solution to Einstein's equations -- the Schwarzschild solution -- in order to construct a concrete visualization of the spacetime manifold. Will this visualization grant us new insight into our higher-dimensional reality? The secrets of gravity are locked away... in The Geometry of a Black Hole.
Contents:
00:00 - Intro
00:50 - The Schwarzschild Metric
02:03 - The Schwarzschild Coordinates
06:30 - Resizing Space and Time
10:48 - Visualizing the Manifold
12:07 - Motion on the Manifold
14:14 - Reconstructing the Classical Gravitational Field
15:02 - The Geometry of a Black Hole
17:22 - Conclusion

[@RecoilTechno]

As a regular PBS Spacetime et al. viewer I am glad to find this channel. I really like the more in-depth explanations and enjoy the way the animation is executed - helps me wrap my brain around these mind-melting subjects.

[@triyanbhardwaj934]

What channels come under "et al."? Looking for similar creators.

[@RecoilTechno]

@@triyanbhardwaj934 Fraser Cain (cosmology), ScienceClic(GR, physics), Isaac Arthur(futurism), History of The Universe (ASMR Space stuff), Wondrium (general & other science)

[@triyanbhardwaj934]

@@RecoilTechno Thank you :) Love HOTU btw

[@trout3685]

What did you learn here that you didn't know before?

[@RecoilTechno]

@@trout3685 I don’t really consider myself as knowledgeable on any of the subject matter, but for instance, this particular video features a more in-depth look at the mathematical aspects.

[@rhythmguild4333]

I always struggled with maths yet I’m obsessed with physics. These videos are great. 🙂

[@artdonovandesign]

I too would _love_ to be able to comprehend the inhumanity difficult math behind Black Holes, S.R. and G.R.

[@miselfis]

@@artdonovandesign Special relativity is pretty simple mathematically. You only really need to know algebra to understand it, and preferably also some basic differential and integral calculus, but it's not needed to understand the basic concepts.

[@j.r.8176]

I'm the opposite lol You can have a subject explained in physics terms and I understand nothing. The same subject explained in abstract mathematical terms and I have a much easier time of understanding it.

[@Ernthir]

@@artdonovandesign "Inhumanity" is a noun. You can't use it as an adjective. Maybe "inhumanely" difficult mathematics. But it is strange to use that word here. Math doesn't have any motive that can be described as being inhumane. You could use the word "inhuman" maybe... If you want to use it to describe how "difficult" the math is would become "inhumanly difficult math". But who cares we know what you mean XD

[@Micro-Moo]

@@Ernthir "Inhumanity is a noun". You are perfectly right. But the entire statement using "inhumanity" is also wrong semantically, and this semantic, and, I would say, methodological fallacy is even worse. Humanity is the attribute of the human. Frankly, every time I see the word "math" instead of "mathematics", I don't expect anything related to real mathematics. 🙂

[@Diaming787]

Every new video I watch about how the geometry of spacetime is constructed, I'm blown away for how Einstein came up with it!

[@mastershooter64]

Well...he didnt completely invent it, there is a field of mathematics that deals with all this called differential geometry that has existed since before einstein was even born, he used it (with the help of several other mathematicians) to formulate his brilliant ideas and make quantitative predictions

[@peterdamen2161]

Unfortunately, the concept of spacetime is wrong 😞

[@stomas4744]

@@peterdamen2161 really?

[@peterdamen2161]

@@stomas4744 Really!

[@Nosirt]

@@peterdamen2161”I am withdrawing my theory on account of dr. Prof. Peter of KZbin comments expert opinion.”- Abe Lincoln

[@taramarielmt]

I followed immediately after watching! This is the most meaningful information I've found so far on youtube! I didn't have the opportunity to realize my dream of becoming an astrophysicist, but my obsession with learning about it has never gone away. I'm so grateful for science communicators who give others the opportunity to understand and learn!

[@trout3685]

Most meaningful information? Really? What is so meaningful? What did you learn that you didn't know before?

[@alwaysdisputin9930]

@@trout3685 This is what I said under DrBecky's video called 'JWST confirms MOST DISTANT galaxy!' _"@Dr Becky - did you see Dialect's vid 'The geometry of a BH'? It's interesting. What I learnt is: Greenland's too big on some maps but you can change it to the correct proportions by saying "shrink it here by a factor of 3.5 & here by 1.5" etc. In relativity there's a thing called a metric tensor which contains those destretchification numbers e.g. 3.5 & 1.5. Around a BH, space's stretched too much so if I am holding my banana, it'd become a spaghettified banana & the metric tensor says [your banana's stretched by a factor of 2000]"_

[@justanotherguy469]

You do not have to be PH.D'd t or ordained by some university to make an amazing discovery. Follow your heart and your dreams will come true.

[@benjamink2398]

@@trout3685 bro what are you on about lmao

[@tursinbayoteev1841]

At 9:42 is the ruler really seems to distant observer contracted when when proper distance increased? Isn't he mistaken?

[@miinyoo]

This is a brilliant visualization. The toughest thing to get your head around (which on its own isn't) is the transformation from Inertial coords to Accelerated coords and back again to demonstrate what's really going on. Otherwise, this makes perfect sense.

[@andyhughes8315]

From a Linear Algebra perspective, I think its transforming the Inertial coordinate vector relative to a change of basis. Then viewing the inertial coords in the new basis. Dr. Trefor Bazett has a video about it here kzbin.info/www/bejne/qWWqdGmwpLp_n5I

[@TristanCleveland]

Yes, that was a crucial beat, and it was a bit fudged. But otherwise excellent.

[@tursinbayoteev1841]

At 9:42 is the ruler really seems to distant observer contracted when when proper distance increased? Isn't he mistaken?

[@-_Nuke_-]

"This makes perfect sense" So can you explain to to us? From this map, I still don't understand the causality of Gravity... Is spacetime that causes Gravity? Or Gravity just exist withought us knowing why, and we simply just generate a map of how spacetime looks around the object that is causing Gravity? If Gravity isn't a force, aka - we have a spherical object that is expanding "outwards" all the time - and thus its surface will eventually "fall" onto an inertial observer... Then WHERE is this object expanding to? It is obviously not expanding towards any of the 3 dimensions of space... And to say that "space is falling in like a waterfall" is NOT answering the question either... IF there is another dimension in which a spherical object - due to internal pressures - can expand its surface towards - then what is the name of that dimension? Is it time? I don't understand...

[@caveman36]

Each episode ends in a cliffhanger, getting you closer to but not quite there to the full picture. Absolutely amazing videos and the progression allows you to actually grasp the concepts easily.

[@dialectphilosophy]

Thank you for watching and glad it helped your understanding!

[@Stargazer10255]

I guess the last episode will also end in a cliffhanger 'cause at some we stop knowing what the duck is happening

[@tim40gabby25]

Even with sound off, subtitles on, this was beautifully clear. Well done.

[@alexandrekassiantchouk1632]

Einstein's theories (both SR and GR) are 50-50 mix of reality and illusion. Reality of time dilation, illusion of objects and space bending. You might need to check story on Medium: Illusions of Einstein and Rotary Blades Curving

[@Bitzy]

i’m watching this at 2am with barely a highschool understanding of math and i just wanted to say that the way you describe things is perfect! particularly the diagram with the hill. i felt that “aha” moment and this video is constructed in a way that i can actually understand the basics of what’s going on! fantastic job

[@ScienceClicEN]

Fantastic video as always ! It left me eager to see you tackle the inside of a black hole, maybe in a next video ? I was thinking about how the scaling terms of the spacetime slices become imaginary under the horizon, and how this could be related to a rotation maybe ?

[@angeldude101]

I've heard explanations claim that space and time flip inside the event horizon, which would actually be fairly consistent with a rotation like from i.

[@darrennew8211]

Check out PBS Spacetime channel. They've done a couple videos on that.

[@nikgracanin6180]

ScienceClick and Dialect are hands down the best non-uni level physics educational channels.

[@davidgoldgruber8541]

This embedding was invented by Rickard Jonsson, PhD, as far as I know. Can not give you a link, because YT deletes those comments instantly. He generalised this embedding to include the interrior and to the Reissner-Nordström-metric. I think that it is impossible to generalise it to Kerr or Gödel or anything 'rotating', but RN is very similar to Kerr.

[@davidgoldgruber8541]

The final boss of black hole visualisation/understanding is Donald Marolf's embedding into Minkowski. In my opinion, that is much better than that 'space is falling'/Gullstrand-Painlevé approach. I wanted to make a video on Donald's embedding, but am I lazy man :/ . I hope that eventually either you or maybe Dialect will make a video about it, to show its beauty to the greater public.

[@nlee1943]

Thank you for the new video! Your team always does a great job balancing visual aids with careful explanations. It is hard to be so clear about a topic as nuanced as general relativity, so I appreciate the time and research you all put into the videos. Looking forward to the next ones!

[@mastershooter64]

An absolutely brilliant deconstruction of the ideas of Riemannian Geometry and General Relativity, this should be shown in every GR class in the world. Beautiful visuals and wonderful explanations! You sir, have gained a like and a subscriber!

[@dialectphilosophy]

Thank you for your support and appreciation! Hope we can continue to illuminate the mathematics and philosophies behind these advanced topics in physics for y'all in the future!

[@garytafoya8859]

Right 🤣

[@PSG_Mobile]

Each one of your videos adds a new piece of a big puzzle. It is very satisfying to realize how they link together to tell the same story. Really great work!

[@trout3685]

Can you explain what piece this video added and what pieces were in place before this video?

[@larrytemen4789]

Do you always tell your car “great work” for functioning? Cause telling an AI channel “great work” is essentially the same thing.

[@genericjoe4082]

Absolutely amazed by the fact that this channel still doesn't have a 100k subscribers. The visuals and explanations are simply wonderful.

[@ruslanlungu2113]

Because out there are not so many "smart" people who really enjoy math Luckly I am not one of them :)

[@realcygnus]

Superb content ! As usual. I've never seen an explanation quite like this.

[@trout3685]

Is it really that much more clear? Things go into the black hole. What did you learn here that you didn't know before?

[@northernalberta]

I don’t even want to imagine how much work went into making the graphics for a video like this, well done!

[@drottercat]

If there were a Nobel Prize for methodical explanation, you would get it. Speaking slowly and clearly is a big par tof it.

[@maujo2009]

This video needs a sequel where you offer a visualization of the Spacetime of a black hole past its event horizon.

[@darrennew8211]

Check out PBS Spacetime channel. They have a few of those.

[@tlldrkhndy]

Watch the SciencClic episode of how Time and Space switch when you enter a black hole.

[@Lord_and_Savior_Gay_Jesus]

Anyone who does offer such a visualization is basing it off of unfinished data or a broad generalization based on our understanding of physics, considering the physics we know breaks down past the event horizon. It'd be like asking someone to create a visualization of God, which is impossible.

[@xaverstenliz8466]

if he can, he get the nobel price 😀

[@maujo2009]

@@Lord_and_Savior_Gay_Jesus I thought the inversion of the spatial and temporal coordinate past the event horizon was part of that visualization. Is that an incorrect assumption?

[@jack.d7873]

An absolutely brilliant presentation again. It's the visuals + mathematical explanations of physics that makes this channel (imo) among the best of human creation. A good teacher is able to clearly explain un-intuitive concepts to those who've never encountered such ideas. It may have gotten a bit technical for complete beginners towards the end, but dialect teacher's masterfully. Spacetime taught like this can change the world.

[@csimet]

Probably the best visual explanation I've ever seen of this topic. Relatively easy to understand. Good job!

[@DenverDonate]

This is the most amazing visual explanation on the topic of how gravity works and black holes. Nothing else on KZbin even comes close.

[@GeoffryGifari]

i don't know if this has been mentioned before, but i think its cool that your narration is not too fast, especially for topics like this

[@Eric-Marsh]

This is very helpful. Something that is mentioned that I find very interesting is that not only time but space contracts near the event horizon. This seems symmetrical to how space expands in regions without a lot of mass. Can you do a video showing how all this works with a rotating mass?

[@nice3294]

This is such a great video, I've never actually seen anyone properly visualise the curvature of spacetime around massive objects to this level of detail/accuracy

[@NeroDefogger]

it's just a sphere, the "curvature of spacetime" is not a real thing

[@jasonbaines7569]

I have study General Relativity for many years, including two semesters of General Relativity in college. It is one of my passions. I would be happy to call out any wrong information in the video, but i can find anything wrong. This is a well done video about the Schwarzchild metric. Great job!!!! Looking forward to the next one.

[@GameADKZ]

This is what im searching since i was still a kid and the only thing that they put on display are just 2d form of explanation and no one except you that was able to put this.. thank you

[@mighty8357]

You are so good at visualizing topics. Excellent work!

[@BangkokBubonaglia]

Awesome video. Thank you so much. You can stare at the equations all day, but to see it visualized this way is truly enlightening....even if slightly wrong.

[@elio7610]

Is it enlightening though? All of the spacetime curvature stuff has made no sense to me. I get the impression we need to completely rework our language for any of these concepts to be explained accurately.

[@flambambam]

@@elio7610 Or... just learn the language of mathematics.

[@elio7610]

@@flambambam Fair point, i guess, still, it seems like language has been failing to keep up with everything. You can argue that is what math is for, yet people still try to describe stuff in english. It seems like an issue that extends beyond science, langauge failing to adequetely describe reality and leading people down all sorts of weird logical paths to argue over fictitious concepts. Apparently, people treat language as an unquestionable tradition and claim it can't be improved. Maybe there is no perfect language, there certainly is language that works better for specific uses than others though. I am convinced language is being treated too much like a religion when it could be more practical to treat it as a technology.

[@flambambam]

@@elio7610 Semantics can be tricky in that regard. The interpretation of verbal language varies per interpreter, and mathematics helps remove that ambiguity. It works well within its own domain, but the translation process between the mathematician and the layperson reintroduces that ambiguity. One practically has to specialize in both mathematics and verbal language to effectively and correctly portray the concepts being discussed. For me, it's easier to develop an intuition for math than it is to put that intuition into words. It's almost like describing a sense to someone that has never experienced it, except we created a new sensation and are now attempting to describe it using previous knowledge. It's hard to understand because we aren't hardwired to understand it.

[@thetinkerist]

I know this is from a year ago, but this video shows one of the best visual constructions of how gravity emerges. I love this! Everyone slightly interested in physics should watch this.

[@openyoureyesandseethefutur5802]

Gravity is pretty crazy, maybe more complicated than crazy, maybe more mysterious than complicated , im glad KZbin is trying to figure it out

[@zair_salahuddin]

Wake up honey, new Dialect just dropped

[@lumi2030]

there are so many dialects nowadays

[@kissrichard86]

especially that you understood, what dialect is about in scientific circles is not important

[@real-one-81]

😢😅❤

[@kulwant..]

😂😊😅

[@SignatureSignsSouthampton24]

So we are not speaking of a linguistical dialect or colloquialism of sorts. What we are really discussing is the speed of light and how exceeding it, may cut you off from the laws of the known universe, or exceed the laws that allow you to perceive those laws visually or mathematically. Personally I think black hole is large fork that spins space-time around like spaghetti, forming large twine like ball of linguini-like universe all rolled up small enough to exceed the laws of regular universe. If universe was a large quilt these would it be spots that God jam a fork into and twist around to hold things in place like tacks or to be like drain pipes for the universe that empty into impossible 4 dimensional spaghetti twirling forks of universe!

[@celtickitty6547]

This is a brilliant way to explain this concept! In university (way back in the 80s, sigh) we were given equations for things like how an event horizon looks mathematically, but there just wasn't this kind of detailed explanation. I really wish I could have gone to school in today's world. We had to use Fortran to write code for our astronomy classes, (another heavy sigh & some slight head banging because, argh Fortran).

[@conformist]

dude this is amazing. as someone who didn’t study physics but always had interest, this is soooo good. thank you and please continue making videos

[@abcde_fz]

. FINALLY !!! THIS IS THE FIRST TIME, in all the videos I've ever seen, where the 'rubber sheet' analogy was effectively replaced with an understandable 3D representation, using the 'multiple cone' model you used. It's about time someone did this. I've been waiting years for it...

[@you2tooyou2too]

The trampoline illustrations, should have the membrane pulled toward the center of mass, not pushed away from it. (sigh)

[@shearemy1157]

I still have to wait a year or two until I can take GR, but I smile at the thought of "gravity is a bunch of rotating bullet-shaped spacetime manifolds that give the illusion of a gravitational field" lol. I remember my introductory QM professor talking about some "folding up" of a geometry with regards to this question so it was awesome to see visually. Also, gonna start calling the tips of bullets "singularities" from now on, thanks. :D

[@dialectphilosophy]

Thanks for watching, and glad you enjoyed it! (And technically, we were imprecise when we used the term "manifolds" in the plural -- it's all actually a single manifold. If you change what radial line you are on, you would sort of "hop" from one rolling sheet to the next.)

[@CosmicCustodian]

Thank you so much for video! You've helped me and many others finally visualise better 3D gravitational effects around a BH. It's been bugging me for years tryna to conceptualise it in my head and this video pretty much gets it on point, bravo dude 👏🏻❤️

[@whirledpeas3477]

awsome comment dude.

[@johnculver9353]

Love your content and while it’s outside my field, I enjoy the challenge of at least trying to grasp superficially if not conceptually.

[@ranganramasamy6820]

The best explanation I have come across for a black hole!

[@leapdaniel8058]

When the whole manifold of spacetime comes to a point, as you mentioned at 15:30, the r coordinate is r=2GM/c^2. The time-time component of the metric tensor goes to 0, so it makes sense that everything converges to that point. But by the same token, the radial-radial component is infinite, right? So it seems to me that if the radial distance of that point is infinitely far away, you'll never actually reach it. Some modern physics discussions talk a lot about the problems of knowing what's beyond the event horizon. But if nothing actually ever gets to the event horizon, then isn't the answer simply that: there's nothing beyond the event horizon? Because nothing ever falls in that deep, as it would have to travel an infinite distance to do so?

[@1300thiago]

To a outside observer it's exactly what happen, but to the free falling to the black hole observer he would travel a normal distance, while the rest of the universe fast foward in time up to the end of the universe... then die

[@CleverNeologism]

You are not wrong. From the POV of a distant observer, nothing ever reaches the event horizon... it slowly approaches it, and dims as it redshifts and asymptotically approaches the horizon. It's not that it's just infinitely far away... it spacetime after all. It's also infinitely in the future. From the POV of the object falling in it takes a finite (and short) time to reach the horizon and whatever is beyond it. Consider the transformations he shows to convert between inertial and orbiting (accelerated) observers in the video. In doing that rotation, and combining it with curved spacetime, the space and time dilations undo each other, and you get a finite distance and time travelled by the falling observer (i.e. they are reciprocals). 2D space is not 2D spacetime: imagine each ring has a vector between 0 (at the distant observer) and pi/4 (tip) attached to it to represent the Lorentz rotation applied in order to keep the orbital lines parallel in the diagram. This introduces the "twist" he shows for inertial observers that fall in.

[@flambambam]

But what about the stellar core that formed the black hole? The matter at the center of the star would already be beyond the event horizon because it existed there before it formed.

[@leapdaniel8058]

@@CleverNeologism (and @Greathigo ) So there's this idea that an outside observer (let's call her Alice) never witnesses anything cross the event horizon, but an in-falling observer (let's call him Bob) crosses it. I have a followup question. Suppose, long after Bob has already jumped in, Alice also jumps in. As we said, in-falling observers cross the event horizon. So Alice must cross it. But now, she also must observe Bob cross it at some point before she herself does, since Bob jumped first. Is this so? If so, it would suggest that there is some non-zero distance from the event horizon at which you actually can witness things cross into the event horizon. Also I'm not sure I understand what rings you are referring to. Are you talking about the green rings corresponding to time axes at individual "points" in space?

[@leapdaniel8058]

@@flambambam My guess would be that, at least from our perspective far outside the black hole, the whole stellar core would be smeared on the black hole surface. Any two particles in the stellar core have an event horizon, right? From our outside perspective it would take forever for one particle to cross into the event horizon of the other.

[@bluescreen1137]

Hi, I'm a little confused when you talk about the motion on the manifold 12:08. I mean that I don't understand why you consider two observers. Why is it necessary to accelerate to maintain the radial distance constant in the first place. Isn't that what is supposed to result. I thought that free-falling objects approach massive bodies simply because if you follow the proper time, that's where their future leads. What I want to say is that the visual representation should point out the fact that if you draw a geode on the manifold then you inevitable would approach the massive body, right???

[@elio7610]

Recently i have been thinking about all the simplifications and visualizations i see in explanations of phenomena, i am not sure if am learning or being mislead. The issue is trying to teach complicated concepts while skipping all the complicated details, the question is: Does any of it communicate an accurate and useful explanation or is it more often misleading people into believing something wrong? Language use can be just as misleading as visuals, so i do not think visualizations alone are the sole concern.

[@PSG_Mobile]

If I got right... The inertial object moves on r direction following the curvature of spacetime, in this case the distance r decreases as it moves on time direction. The only way to keep a constant r distance in this curved spacetime is to accelerate in the opposite direction. The non inertial observer is not necessary to explain the motion of the inertial object, it is just to show how the inertial object moving on the curved spacetime looks like a free falling object from the point of view of a stand observer in r direction.

[@dialectphilosophy]

Hey, thanks for watching! You're correct to point these issues out. One of the first things we learn in General Relativity is that objects follow their natural geodesics on the curved spacetime manifold -- but clearly here the inertial objects do NOT follow geodesics. The typical answer most physicists will give is that because we have used a euclidean surface to represent a hyperbolic one (spacetime distances involve a negative sign) geodesics will take a direction "opposite" to what we expect. However we suspect that the mismatch between geodesics and inertial worldlines are more related to the fact that this surface is constructed from the accelerated perspective (which would constantly introduce an "offset" to the manifold's straight paths, making them non-straight). Many physicists, even the highly credentialed ones, don't understand acceleration in relativity very well, so it's possible once we re-construct the manifold from an inertial perspective, geodesics and worldlines will match up. We hope to resolve this issue and provide a fuller explanation in future videos. As to why one needs to accelerate to maintain constant radial distance, we suggest checking out our video "The Sky is Falling Up" for more on that.

[@dialectphilosophy]

@@narfwhals7843 In the original script, we addressed this issue, but for time and flow and comprehension purposes, we cut it. Mainly, because it involved a whole discussion about acceleration in GR, and, well, you know how well that's gone over in prior videos. It's not unfair to accuse us of being misleading here, as the mismatch between geodesics and inertial worldlines here is definitely a major omission and source of confusion. However, unlikes *some* channels, we are fully prepared to address why we made such an omission, and moreover, do intend to clarify it in future videos.

[@bluescreen1137]

@@dialectphilosophy Thank you :) Now it's much clearer. I rely more on intuition because I don't find enough time in my life to study physics properly. So when you did that transformation there, my brain stopped.

[@recifebra3]

This is so well done man!! It's crazy people figured this out w/o proper visuals - I guess they just figured it out in their heads.

[@TeamSkeptic]

This is definitely one of the better visualizations on how gravity is derived from the tensor equation. Good job. A future video suggestion : Explanation of how the Schwarzschild equation suggests that the event horizon has an escape velocity of c, and how that is merely a mathematical convention. As traveling faster than the speed of light, if it was possible, wouldn't allow you to escape out of the black hole, beyond the event horizon. I've seen a few good explanations of it, but few have the presentation quality that you display. Again, great video!

[@willo7734]

Wow, i’ve been interested in relativity for decades since I was a teenager but this is the first time I’ve seen this explained where I can grasp it intuitively.

[@NeroDefogger]

same, I could understand it until I realized that... there is nothing to understand, you can't understand something that is not real

[@FulgenceMalvenue]

@@NeroDefogger Except that black holes are real, and even if they weren't, it would still be possible to understand them.

[@NeroDefogger]

@@FulgenceMalvenue I wasn't talking about black "holes" (neutron objects)

[@FulgenceMalvenue]

@@NeroDefogger what were you talking about, specifically? What is it that one can't understand since it's not real?

[@NeroDefogger]

@@FulgenceMalvenue einstein's "relativity" or what I call absolutivity

[@GaryFerrao]

What software do you use for your animations? It's really helpful to the explanations.

[@poseidonguy3940]

Doug Demuro's tongue is huge?

[@StatsScott]

What an extraordinarily informative video! I’ve watched a lot of explanations of black holes and spacetime curvature but this one is far and away the best yet.

[@user-ot7lv8su1b]

You sir have no idea what you have done here. Best visiual/explanation i've ever seen. You're doing Gods work.

[@annegajerski-cauley8324]

A very accurate and lovingly done production -bravo! I would have no reservations in presenting this to an introductory relativity class. Bur as they say, and you imply, good teaching involves the gentle stripping away of simplifying lies and distortions.In this context I would simply caution any student to not take the use of the eyeball, in representing the observer's local frame, too, too literally. The issue is one of comparing events as located in highly useful co-ordinate systems for the manifold, like the Minkowski coordinates used throughout here, using measurements such observers might make. This should not be taken as what would literally and immediately be seen by a local astronaut, as light travel time and path over macroscopic distances would as a rule give distorted personal results. The student must be reminded to think in terms of measurement possible in some local (proper) frame (free-falling or not), as if "present everywhere at once" at some proper time instant, to avoid certain pitfalls (alluded to right from the start). Notwithstanding, a very nice primer on actually "handling" curved spacetimes! All the best, D. Barillari, PhD.

[@jimmytiddlytoo8160]

If you fall into a supermassive black hole you’ll see the whole universe pass through billions of years before you’re spaghettified

[@petersmythe6462]

The funny thing is that even neutron stars we can perfectly well see can be inside their own photon sphere, meaning they negate or invert centrifugal force. It's not just that light isn't fast enough to orbit them that close. It's that their surface geometry is flat or concave so no amount of speed will actually let you escape horizontally. Similarly, as you approach a black hole, it is no mere optical illusion that the universe sinks into an infinitismal point and the event horizon becomes all-encompassing. The event horizon is in fact deeply concave at every point.

[@lewisheasman]

You lost me at 0:01

[@kguynchkh]

Underrated comment

[@DemoniteBL]

What's with all the anti-science comments here? lol Sad to see just how ignorant people can be. Good video btw.

[@darrennew8211]

This is probably the best explanation of spacetime curvature I've ever seen, as a layman.

[@YokoX23]

I like how you're doing this slowly enough for anyone to pause and take notes.

[@Ohrapell]

Shit Im so high and This is a bit of a different video than I expected. The info is not like science pops, it is clearly in-depth. Since I am interested in the topic of quantum physics and astrophysics, I like this kind of content very much. But not this time :) It lasted me 5 minutes

[@nicreven]

This made no sense until the end At which point everything made sense I've never considered the idea of every object having an event horizon before. Great vid!

[@C.K.MillerPoet_Extraordinaire]

I have insane trouble understanding high school algebra, and I failed my first attempt at the GED math test, but for some reason these videos explaining high math concepts are super fuckin interesting, and easier to understand than finding the fucking goddamn formula for finding the slope of a line. Thank you for being a good teacher

[@ignetiusjrelly]

Just for this topic alone of Geometry of Black hole you have me as your subscriber. Very informative content as well. Great Job.

[@Mateolochi]

What a masterpiece of explanation. Great video!

[@gahan09]

One of the best visualization of Gravity and Black Hole............ Just Awesome.... You can even explain same concept with pencil and sharpener...

[@SritharanSrikanthanBigBoss]

You must be a genius..Animations and explanations are out of the wold...

[@feynstein1004]

Damn, another channel on par with Science Clic English. What a time to be alive 🤩

[@aquamanGR]

Very nice presentation. This is one of my favorite explanations of the Schwarzschild metric.

[@causeitis]

Incredible explanation and visualization! Keep making more, this should find a bigger audience!

[@Dekoherence-ii8pw]

This bit of the visuals 14:20 blew my mind. That's hella trippy!

[@armorkny]

I really like the pauses in this video. Gives you some time the sink the information in. A lot of youtube videos just chungus their way through the video like adhd children.

[@mwdiers]

Ok. This time I finally got it. It all clicks now, and I see exactly where you have been going in your explanation of how mass acceleration + space-time curvature = Newtonian gravity. Curvature of the space-time manifold balances acceleration such that for any given mass (the earth, for example), the physical dimensions of the mass become stationary relative to any fixed point in the manifold. The explanation was right there in your diagram of the inertial observer vs. the accelerating observer. As the mass is accelerating, it may not blow up, but my mind sure has. Well done!

[@HansangVibration]

whoa this video was actually EXTREMELY well done! The visualization was impeccable, especially that of the inertial frames of reference! Great job

[@extreme4180]

Damn the animation, the voice, the explanation everything's so good

[@juniorcyans2988]

This 18 minutes video took me hours to finish. Thank you so much for making such a profound and complicated topic understandable! So luckily I found this video when I searched for topics on black hole, as I'm learning relativity and topology this semester!

[@darlananan7201]

One of the best videos describing the effects of the curvature of space time with visualization i've ever seen so far

[@AriannaEuryaleMusic]

This video explanation is AWESOME.

[@benallan5835]

this was genuinely insane, such a cool visualization

[@RsklnkvX]

...that was Awesome!! ...wow, what a way to start the new year... the clarity of both thought a speech is admirable ( I think a generated voice would be incapable of that "Schwarzschild" pronunciation, but I could be mistaken. 😊) ...ty so much, glad to have found this channel.

[@Agnom]

Kudos to you. This has got to be the best visualization of the spacetime warping at the vicinity of any large bodies.

[@BlastFXTrading]

I don't know the math behind these ideas, but I'm watching, consistently.

[@PrometheusZandski]

I like your video. Starting at 8:20 your clocks were running incorrectly. The little hand was moving one rotation an hour and the big hand was running one rotation every 12 hours. Should be the other way around.

[@davidmcneil2296]

9:06 the way you stretch and shrink the matrices in these matrix and how you have it in a grid, actually makes sense whe it comes to how gravity can distort time and space. The way our stretch and shrink a square in a graph just made so much sense when I was watching this. It made me think of interstellar.

[@TLMuse]

This video strongly reminded me of Andrea diSessa's "wedge" formalism for understanding general relativity, as described in his 1981 article in American Journal of Physics, "An elementary formalism for general relativity." This approach has recently be extended by Robert Scott in a 2021 paper in European Journal of Physics, "Visualization of flat and curved spacetimes with simple cartography tools." Viewers intrigued by this presentation and wanting further details should seek out those articles. As an astrophysicist who has done some work in cosmology and high-energy astrophysics, this has long been my favorite way to understand and explain spacetime curvature. -Tom

[@dialectphilosophy]

Do you have any links to those works? It'd be great to share -- the only work we're aware of that resembles this so far is that of PhD Rickard Jonsson.

[@jeandesroches2285]

Elegant, gracious and sophisticated. The dialectical class at its nec plus ultra. Bravo.

[@DanNowlan]

Great explanation with just the right amount of math for the casually curious, but you gotta fix those clock hands!

[@jsEMCsquared]

Thanks for the visualization gravitational anolomilles are hard to imagine. You spelled out a neat way to imagine them. Your thumbnail pic showed another way to also visualize the effects in 3 d. I would like to see that.

[@davidgoldgruber8541]

Rickard Jonsson's embedding of the Schwarzschild metric into an Euclidean ambient space (presented in this video) is very cool, but Donald Marolf's embedding of the Kruskal-Szekeres metric into an ambient Minkowski spacetime is waaay more informative and better for visualisation, in my opinion. That one does not contain these annoying coordinate-singularities, and is geodesically complete. (Explains black holes, white holes, Einstein-Rosen bridges, sphaghettification, gravitational time-dilaton/redshift and how space and time 'switch places' below the horizon at the same time, and finding geodesics on that surface is as easy as finding them on the sphere.)

[@dimitrispapadimitriou5622]

Yeah, this coordinate singularity at r=2Gm of the Schwarzschild coordinates gives the wrong impression that there is a "discontinuity" there, while spacetime geometry is perfectly smooth on the horizon. And this presentation leaves outside the interior...

[@dimitrispapadimitriou5622]

@@narfwhals7843 No, there is not a discontinuity in the *spacetime geometry* . This coordinate "singularity" is only an artefact of the Schwarzschild coordinates. It does not appear in other coordinate systems (e.g. Kruskal, Eddington/ Finkelstein etc). The curvature scalar ( that is independent of the choice of coordinates) remains finite on the horizon ( it only diverges at the curvature singularity r=0 ) and the transition of the r=constant hypersurfaces from timelike outside to spacelike in the interior is smooth ( the horizon itself is a null hypersurface). Events in the interior ( the trapped region) cannot influence causally events outside , but that does not imply that something funny happens with the geometry on the event horizon.

[@dimitrispapadimitriou5622]

@@narfwhals7843 If you're talking about the light cones as they appear in a diagram that uses the Schwarzschild coordinates ( that shows a discontinuity near the horizon, both from outside and from the inside), then this "discontinuity" is, again, artificial. Locally, a free falling observer won't notice anything when crossing the horizon. Only a hovering observer, that tries to remain just above the horizon accelerating madly could notice that the outside visible universe seems " compressed" to a 'dot'. In an Eddington/ Finkelstein diagram ( like the one that was drawn by Penrose in his famous Nobel prize winning paper) it is clearly shown that there is no discontinuity ( the light cones bend towards the interior in a continuous manner). That's why I mentioned before the smooth transition ( from timelike to spacelike) of the constant r hypersurfaces from outside to the interior, respectively ( this is a more accurate phrasing of the "switching between space and time" as the pop science media call it ). This transition is directly related with the causal structure. The "one way only" transmission of signals is a characteristic of causal horizons ( not only those of black holes, but also the Cosmological event horizons like in a deSitter spacetime). There's no real discontinuity in all these event horizons. They are lightlike hypersurfaces, like the light cones are.. There are , indeed, horizons ( the so called Cauchy horizons, like the ones in the interior of rotating black holes ) that are unstable and they can develop "weak null singularities " , so they're not smooth , but these are another story.

[@muhamamadabdussamad7135]

One of the best explanations I have ever seen. Thank you

[@dimitrispapadimitriou5622]

Using the Schwarzschild coordinates alone is not a good choice, because of the "coordinate singularity" at r=2Gm ( at the event horizon). The interior spacetime geometry is totally ignored in this video. For those interested, the interior *spatial* geometry of a Schwarzschild black hole is that of a 3-tube ( the 3-dimensional analog of a cylindrical surface) that is the product of a 2-sphere times the line. These " 2-spheres " ( that are cross sections of the spacelike hypersurfaces r=constant, for r

[@98_sam_]

This is the first video I see from you, you are a genius! If you haven't done so already could you make the visualisation of the Big Bang? Everywhere it's visualised as a cone stretching outward from a singularity in one direction but I guess I'm missing the bigger picture

[@ariannasv22]

This gives me educational video you've seen at school vibes but more entertaining

[@arjunv]

Had thought a lot about what space time curvature actually means and the impact of black holes on them, and wrote an article on the topic. What if blackholes basically act as a pinch on the space-time, adding a pull to the expansion of space time? Wouldn't that lead to miscalculations such as the age of universe? And if that's the case, the super massive galaxies of today would be miniscule blackholes formed right after big bang, as they expand with time. Their presence could have led to more mass accumulating near them, causing the formation of galaxies. As they become bigger, this "tension" would increase to a point that the gigantic black holes would pull everything back and a big-crush would follow. Leading to another big bang.

[@Lombey84]

Really looking forward for the next dive.

[@50secs]

This is a marvellous video. Thank you for this.

[@KaiseruSoze]

Because GR runs into the problem with a singularity, wouldn't you say GR is flawed? Or at least "not that general"? You've put a huge amount of work explaining Einstein's perspective and great job BTW. But... GR is highly dependent on a belief that there is a single continuous object we refer to as "spacetime". It's not wrong in that context but it becomes a "favored frame" when you consider the measuring context of an electron, or proton or galaxy or a cosmic frame. From your discussion so far I'm getting a message of a conviction - like you're taking a really long time to say "IT"S CURVATURE! NOT FORCE!". That's an argument and yes you have done a great job with your presentation. And as part of a course in Einstein's GR this is great. But you really should make it clear up front what your intention is otherwise you are wasting everyone's time. I have been watching only because, in earlier videos, you seemed to have a different conviction - something like new physics? And so far I'm not seeing it. If I were a physics instructor I'd say that GR is interesting but it's a dead end if you want to understand... And I'd stop here and point out that this was what Einstein often wrote about. He said that it was an epistemological problem. Not a technical problem. The same goes for QM. And I'd say the same with string theory. From a technical perspective they're fine. But they don't help with the "understanding" part. But from a heuristic perspective - it's progress... but in the wrong direction. Ok, from my heuristic perspective.

[@angeldude101]

Probably the most interesting thing I noticed is that areas seem to be constant. No matter how close you get to the surface, the area of a given grid square remains the same, the stretch of space perfectly counteracting the compression of time.

[@tappetmanifolds7024]

Well observed. You might like you tube videos describing Nash's embedding theorem.

[@frankelkjr8041]

NGL it was a bit difficult to comprehend 1st time watching, but I never saw the geometric P.O.V of a Black Hole! this was Brilliant! This kind of remind me of "ScienceClic Eng"

[@neri4950]

Your video is AMAZING. The only source out there on the internet that truly explained to me space-time curvature and black holes. Hats off, respect, and keep up the fantastic work and videos.

[@gittesilberglarsen1262]

Those small clocks depicted are weird - the short hand moves faster than then the long hand. Would be fun to have such a clock to trick the observer.

[@JonathanRegalo]

I greatly appreciate the time and effort that it takes to create these videos. Very well done.

[@mawage666]

Stellar video man!

[@Zeke-Z]

Visualizations are very good, great video!!

[@martinlisitsata]

in being an amateur astronomer as a hobby there is a certain indescribable joy in the mathematical part of my hobby . meaning i understood nothing from the non-picture part of this but i loved it all the same

[@pheargoth]

This is an excellent video. Your graphics and diagrams of some pretty complicated stuff (to me at least 😆) are excellent. Thanks!

[@yourmomma7869]

I have to take a walk after this video. How anyone can figure this stuff out is amazing.

[@HitBoxMaster]

Very impressive. The visuals were amazing!

[@contessa.adella]

Easy to understand the components…hard to mentally hold onto it as a vision…but I think I’m there and better understand why time dilation moves objects through space toward mass. I see time as being the same ‘thing’ as length, just orthogonal to the three we can see…a physical dimension…it makes sense when you stop seeing time as a clock and regard all four dimensions as complete whole homogenous continuum. Most especially poignant when you realise time rotates into the spatial axis and once past the Event horizon your ‘future’ becomes a direction, inward! Fascinating Jim.