The Meaning Behind the Black Hole Equation | Physics Made Easy

[@tatjanagobold2810]

You are honestly doing a great job on bringing "complicated" concepts closer to non-physics students or people who claim to not understand physics! I want to study physics in the future as well and you have always been an inspiration for me :) wouldn't mind some more physics-maths related videos!😂😉

[@_kantor_]

@@ParthGChannel i would love more like in depth videos... great content man! quality education

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@Best_yet_is_2_come]

@@Igdrazil r=R

[@Igdrazil]

@@Best_yet_is_2_come No

[@Best_yet_is_2_come]

@@Igdrazil Landau & Liftshitz used it in 1975

[@jones1351]

Great stuff. For me physics/math is the the beautiful woman who said, "...but we can still be friends."

[@AstroB7]

jones1351 good one :)

[@globaldigitaldirectsubsidi4493]

you just have to try harder

[@pranayranjan3777]

So it's one sided love means u love Physics but physics doesn't love u

[@jones1351]

@@pranayranjan3777 Precisely. I came from somewhere back in her long ago. A sentimental fool don't see trying hard to recreate what had yet to be ...😎

[@Godakuri]

@@globaldigitaldirectsubsidi4493 trying harder has nothing to do with anything

[@Arkamfrz]

Now I understand the meaning of " If you can't explain it simply, you don't understand it well" Great job pal. Very clear explanation of this complex equation

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@ThisisProgrammer-xi7qt]

- Einstein

[@davidwright8432]

What you do here is very valuable, particularly for people who haven't gone beyond high school math or physics. Without showing how to derive, or solve, the equation, you make clear what it's about and how the individual terms contribute to the overall picture. You show what we need to know to solve the equation, and how the overall meaning of the equation is built up. By comparison, solving for particular situations is grunt work! Without the ideas - no equations.

[@saftheartist6137]

Excellent video! 👍 You simplified such a complex topic and kept it concise, without unnecessary jargon.

[@inderjitsingh4588]

This is the guy we all need an hour before exam.. ☺

[@fortunehacking]

I've literally watched 50+ hours of lectures on GR on YT. The way YOU say it in your videos...makes related concepts come together very nicely. For example: You said..."We're no longer measuring coordinates in space-time... we're measuring events..." It's like an observation that causes 10,000 languishing superpositions to collapse instantly into coherent thought. I go.... "ohhhhh, so that means..." Idk..bad analogy maybe... Either way. Thank you.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@adityapandey9639]

You are doing a great job😍... Thanks from India 🇮🇳

[@michaeledwardharris]

Parth, I've had some awesome teachers in my life. You are notable among them! Really learning a lot from your videos. Thanks 😊.

[@arunjanarthanan6380]

its beautiful how you present so much so humble! the beauty of what we do not know prevails at the end :)

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@AgentWD40x]

Thanks for your explanation. As an amateur trying to solve these types of equations, I always thought at some point that I was supposed to integrate it. I had no idea I was actually looking at a coordinate system.

[@jenromeave4793]

hey! i’ve been loving your videos which are very informative and concise! but, if ever, would you create a video detaling how exactly physicists are able to come up with a theory? including the mathematical formulae? thank you!

[@everythingpossible8185]

Dude u are doing a great job and im feeling bad for u cause u have so much less subscribers I'll tell my buddies to see it too. Keep it up . I'm a great fan of physics and maths and I'm in the 10 class I m much interested in quantum physics and I learned calculus in 9 .

[@MrLethalShots]

Very educational video! :) Bit of trivia: a rotating black hole actually has two event horizons and a singularity shaped like a ring. If you navigate through it properly you can even come back out of the event horizons or go through the ring singularity and possibly come out at a parallel universe. Closed time like curves are even possible inside the inner event horizon so you can potentially meet your past self. If you get sufficiently close to the outer event horizon (a region called the ergosphere) of the rotating black hole and throw a mass in the opposite direction of the rotation you can even leave the ergosphere with more energy than you had originally going in. This extra energy comes at the expense of the black hole's rotation. So rotating black holes are a potential source of (limited) energy :) Edit: btw this last thing is called the penrose process

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@dimitrispapadimitriou5622]

Actually this is the Kerr solution, that describes an eternal , unperturbed rotating black hole . Realistic rotating black holes, that originate from collapsed matter and are not isolated, are similar to what you describe, but with the important difference that their inner region, in the vicinity of the internal "Cauchy" horizon , is actually unstable: It doesn't probably contain a ring singularity, or closed time like curves etc. There is a " weak null ( light like) singularity there ( or even a strong spacelike singularity, or both; it depends on the details), as all the calculations have shown. Interestingly, it was R. Penrose the first who pointed out this kind of instability ( initially for charged black holes, that have also two horizons).

[@kartikeysharma]

Honestly this is one of the simplest explanations of the phenomena that one could come up with without losing a lot of the mathematical essence. A job well done. Although, I have to point out a small error, which many of us tend to overlook even on a good day. At 5:28 you specify the Polar angle to be phi (φ) but at 6:28 you write the metric with theta (θ) being the polar angle. It doesn't impact the rest of the explanation, as you started with a mathematician's definition and changed to a physicist's definition, but I felt like it should be put out there for anyone who also spotted the typo.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@kartikeysharma]

@@Igdrazil Bruh

[@SabrinaXe]

You're good at this, you should make A level CIE videos for students struggling in a levels

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@bhuvaneshs.k638]

Dude this channel is so amazing

[@satyamkumar567]

U r the most amazing person on u tube I have ever seen

[@calimaulud5708]

Man, because of you I gained courage to pursue astrophysics. Thank you

[@soumikdas3909]

Hey can you help me i want to study astrophysics

[@Dan__S]

Thank you. So many other videos are dumbed down and they totally omit accounting for the difference in time as you approach a massive body and further time difference due to relative velocities. Over millions or billions of light years that kind of thing tends to add up.

[@rgriffsf]

Wow!! I previously thought I would never understand Mathematics under the complex physics equations I have seen numerous times in the past. Thank you for explaining from Pythagoras (2D) to 4D. I get it now. Great job!

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@lol-rw7yd]

Extraordinary man love it

[@Govstuff137]

Ok Thank you. It's 5am i should be asleep. But I enjoyed this video. I'm looking forward to seeing the rest of your videos. Do you realize how fast you talk? I am hoping you might do a video on Time Compression. Unless you have already and I just haven't gotten there yet. Thank you for your time. 🖖Live long and prosper!

[@solapowsj25]

Thanks for making physics interesting.

[@ellenw.lovesyou1740]

I like this video. Sean Carroll made a 60 Minutes Video perfectly well explaining every part of the famous Einstein Equation - for people who do not know anything (talking about anything above highschool level) about math or physics. You can learn a lot from his lecture. He is working with 4x4 Tensors, he goes deep into the math but I must say his lecture some levels above yours. It IS possible to send people inside Riemann, Schwarzschild etc. he even added some jokes and talked slowly. I think you have to improve on your didactic. Kind greetings from Germany.

[@BobK-NH]

Great job explaining a mathematically tough concept. According to biographies on Einstein, even he had to seek help with the math of his field equations. Would a rotating black hole’ s effect on space-time be in any way analogous to the effect of negative mass on space-time ? I think you see where I’m going with this( Alcubierre’s geometric manipulation of the field equations) Great topics for future videos are his equations, Casimir Effect and York time. Thanks for bringing science down to earth.

[@julioalvear1641]

Ah! Warp drive.....moving (warping) space-time to travel...yes that would be nice explanation videos.

[@Prometheus7272]

To your first question no negative energy is not yet known to exist and the Casemir. Effect is not negative energy.

[@BobK-NH]

Prometheus Yes the Casimir Effect is not negative energy but rather on the quantum level negative energy density. There is another theory that the attractive force between 2 plates is nothing more than caused. by van der Waals attraction.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@ehsanullahhassani5102]

Nice video. I had difficulty understanding this equation in my college. It was confusing to me till this day. Now after watching your video it completely makes sense.👍👍👍

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@shivamSharma-ml5xg]

I really liked how you described it. i would like to see more of your videos. love from india

[@LivingWaterEternal]

Amazing presentation.

[@MsDilan2009]

Awesome. After watching your Vedio. I understood it .

[@casualinfoguy]

That was a brilliant explanation. I knew where you were going with it at around 1:57. Anyways, where were you when I was an undergraduate? I would have become a physicist, instead of a computer scientist. Btw, I like your haircut.

[@andrewevans5761]

It would be so nice if you gave us a numerical example in any such video.

[@Li.Siyuan]

Beautifully explained, thank you.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@aniket1090]

Thanks for simplification .

[@mmmk6322]

When spacetime becomes timelike. Oh yea that will be a very interesting video!

[@acatisfinetoo3018]

This is actually really interesting. Even Blackhole Chan would be pleased:)😂

[@harshittiwari4487]

Blackhole chan is kawaii 😊

[@achmadrizaldanisya9517]

the first of your videos that i need to rewind

[@69erthx1138]

Using S_2 as a standard sphere, the projections onto the surface can be arbitrary combinations of polygons, that would be animated with angular restriction for the surface (boundary). Going to S_3 the projections are polyhedrons, with the animating coordinate (aka, degree of freedom that no one seems to understand).

[@The_dead-guy]

I wanted to understand the equation at the end which you said was required for rotating spherical objects

[@wulphstein]

It would be important to try to connect the geometry of black holes to wave functions. Wave functions have all of the properties you need to be "building blocks" of spacetime. If you could do that, then you could use quantum entanglements for analogues of wave functions. If quantum entanglements are the building blocks of spacetime, then theoretically you could create artificial gravity fields using quantum entanglements.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@The_Shrike]

I’m curious, for determining the interval between two events in space time, what are the units in the final result?

[@floydnelson92]

either use a vector containing the time component and the spatial component or use the fact that the speed of light in a vacuum is the speed limit... and most physicsts will multiply the time component by the speed limit c, so that it transforms into a distance measure, or divide each distance by c to get time measures. Consequently, this is like one second equals 299,792,458 meters, so on a Minkowski spacetime diagram where time moves up, a 45° angle either to the left or right is moving at the speed of light and anywhere in-between is slower than the speed of light.

[@jayjayf9699]

Parth can you do a video on what a tensor is and tensor calculus?

[@ganeshikhar]

Parth Sir ...u explain nicely up to the equation ...but it will be very nice if u focus more on that equation itself. May be create a separate video. I also saw ur couple of other videos. There also u did the same.😌

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@cloudkicker-gx7gb]

Really enjoyed that thanks

[@Spiritualcreator]

What is the ramanujan equation for blackholes?

[@immortalsofar5314]

I did something similar to the 3d Pythagoras problem to set 3 angles (shoulder horizontal, shoulder vertical and elbow) to move the tip of a robot arm to a given x,y,z co-ordinate. Just use the result of 2d xy into 2d (xy)z.

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@BillySugger1965]

Parth that’s a superb intro to the mathematical concepts underlying GR. If you haven’t already, could you post a video taking us a step further along the road, without doing a full undergrad maths/physics course, in the vein of your superb series on Maxwell’s Equations? Maybe take the equation Brian Greene posted and show what the terms represent? Thanks for all you do!

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@martin-hollingsworth]

I thought algebra was always my strong suit, but you sir have just blown my mind ..

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@inboccaallupo14]

Please make a video about differentiation and integration

[@kenantahir]

thanks for the explanation

[@kayeassy]

Well there is a slight mistake if I may point out ... The choice of your theta and phi coordinates is inconsistent with the formula of the ds ... It's really very minute mistake... You're doing a great job ... I really enjoy your videos

[@thewhizkid3937]

How so, explain

[@rajdipbandopadhyay1291]

2:20 take AB as a VECTOR AND FIND ITS MAGNITUDE,this will be the ans. For ex. Vector AB = X i^ + Y j^ + Zk^ then the length |AB| = rt(X^2+Y2+Z^2)

[@DesertKnight1]

Mathematics is the key tool to unlock the mysteries of Nature and Universe with physics it creates an astonishing stuff which blow your mind .

[@rajvikramnema926]

Do anybody know how can i use similar text animation and graphics for my videos

[@aman-bd2ub]

so well made. so sad to this not spark up 😭

[@singhanianilesh]

can you show how equation for wormhole connects two distant points close at certain conditions. help visualize in lower dimensions

[@richardshelton-dca8810]

How does the equation take into account that at the event horizon the delta t (the time interval) goes to zero in the inertial frames of particles at the event horizon? To me, this would suggest that the mass of the black hole exists only at the event horizon as with no time there is no 'falling in' (that takes time) to the black hole at that point. There would be no difference in the gravitational effects external to the black hole as a sphere with all the mass at the surface acts as though the total mass was at the center point of the sphere to anything outside the sphere. For rotating black holes, again, no difference in the effect on space-time as the mass would still 'drag' space-time in the same manner. It would also check against the Hawking Radiation as all the quantum information would also exist at the event horizon, meaning that quantum data could easily affect any particle pairs formed near (within a plank-length of) the event horizon.

[@thevibe8065]

Where can I get some physics formula sheets?

[@bacakomen6019]

Please explain charge density in 3d dimension calculation,and cosmology

[@FutureAIDev2015]

So the equation relates something about the gravitational field in a region of spacetime to the four-dimensional “distance” between two points in that region?

[@materiasacra]

In General Relativity gravity IS the warping of spacetime. The fact that the formula for finding the interval between two nearby events is modified compared to the 'pythagorean' recipe is the mathematical expression of this warping. If you want to speak of the 'gravitational field' (which is a perfectly ok thing to do in GR), then it is the collection of coefficients on the right hand side of the equation. For the Schwarzschild case: -(1-2GM/r), 1/(1-2GM/r), r^2, and r^2sin^2(theta). These coefficients are components of what is called the 'metric'. If you know the metric, then you know everything there is to know about the (curved) spacetime. What GR does is describe gravity by making the metric 'come alive' as a dynamic entity, under the influence of the stuff in the universe. There is an equation that connects the metric to the energy and momentum of the stuff in the world: the Einstein equation, not discussed in the video. What Karl Schwarzschild did is solve the Einstein equation for the static case with spherical symmetry, and he obtained the metric shown in the video.

[@cmtro]

Excellent !

[@captainhd9741]

Wait wait wait. 2:40 at this point why did you treat the extra dimension as being spatial like cdt because the 4th dimension for time isn’t spatial so it can’t be used in 4D Pythagoras???

[@wRICKyRIZZ]

It seems since space and time is on multiple curvatures, (causing gravity right?),like waves in an ocean, a black hole seems to be like a horizontal underwater hurricane in a sense going through those waves aka space time curvatures instantaneously or it seems to be proof that we could theoretically create a wormhole to instantaneously go through these curvatures of space and time and visit the future, past, or different moments of the present

[@RAJESHSK-ch9uc]

Sir please make videos about calculus integration derivatives

[@mehdizangiabadi-iw6tn]

If the space of a black hole is radioisotope, how are its dimensions and volume measured?

[@cesarjom]

You made a mistake at 5:30 where you label the spherical coordinates. You must switch the theta and phi angles in your coordinate diagram IF they are to match the equation for the interval you defined at 6:24 Also later you state mass results in gravity which results in curvature of spacetime. It is actually in the other direction, mass curves geometry of spacetime which in turn results in what we observe as gravitation (forces of gravity). And yes, that is correct the Kerr metric is the more accurate model/geometry needed to represent a rotating symmetric black hole.

[@CapiFlvcko]

U the best dude

[@triptithakur1590]

Plz Make some more video about black hole equation....

[@jishnun4537]

just beautiful !!

[@anjalishekhar1]

Very good!

[@aldinhaswari1420]

why the sign of time term is negative and space is positive?

[@aimeeaveys]

1:55 imagine that the diagonal line that comes out of point A and goes directly below point B is da^2 so da^2 = dx^2 + dy^2. makes sense? Now, if we add da^2 and dz^2, it get us ds^2 for the same reason da^2 = dx^2 + dy^2. Finally, if we substitute da^2 for dx^2 + dy^2, we get ds^2 = dx^2 + dy^2 + dz^2

[@MisterLists]

Why is the schwarzchild metric different across sources?

[@MrLethalShots]

Hey I don't mean to be rude but you defined phi to be the incline angle at 5:33 and then switched it to the azimuth angle at 6:33.

[@prathamkardam6442]

oh well I am a biology student still I could understand it this just proves how well you explained it...

[@sriharshaboddu2362]

The question of human should never stop , after seeing this I realize this is still alive

[@KritikX]

you are good teacher

[@Nikos10]

Does spacetime bend towards a fifth dimension?

[@humansnotai4912]

This equation really shines when it comes to black holes - haha...very funny.

[@rubentamang1050]

This helps a lot.. Thanks

[@ayushikaushik5587]

Please make more videos on general relativity

[@eeshanghosh1605]

please do more of it

[@seyencho]

So is the ds in the Schwarzchild Metric a geodesic? And, more interestingly, is it invariant like SR's spacetime interval and the Pythagorean Theorem is between reference frames? Is it invariant when an observer is experiencing different amounts of gravity relative to another? If so, does this mean that we can use this formula to find coordinate values between reference frames--for example, Time Dilation?

[@alijoueizadeh8477]

Thank you.

[@mentallingesh6572]

2:03 this comes in class 11th to find the magnitude of the resultant of two vectors in three dimension

[@arjyadebsengupta8159]

You are Einstien

[@asmrenjoyer2016]

@@arjyadebsengupta8159 Einstein is him

[@angelcosta4383]

I can relate hahaha

[@jeremiahlethoba8254]

the event horizon of that m87 black hole is about 28 billion km (according to my Google search) in diameter, so if you do calculations you will find that the fastest spin of the black hole event horizon will only complete one revolution every 3 days...does that spin count as significant

[@ratnakarahuja4409]

Tell me something about the prospects of Physics Masters or PhD

[@user-vr4ud8go2c]

THANKS SO MUCH

[@HimanshuSingh-ho1xh]

10:40...🙌, True...😅

[@bd1487]

Please explain why points and events are different

[@Zodiaczero2]

In the context of relativity, the statement "everyone can consider themselves to be stationary" means that from the perspective of any observer, they are at rest and everything else is moving. To understand this concept more intuitively, let's consider a function on an (x,y) plane. Now, let's add a new coordinate y' along with the curve. From the point of view of the curve, it is stationary in the y' coordinate. This means that no matter how the curve is moving in the x-y plane, it is always at rest in the y' direction. Similarly, in the (t,x) graph of special relativity, we have the equation c^2𝜏^2 = s^2 = (ct)^2 - x^2, where s = c𝜏. Here, s is the dimension that traces along with the path of a moving object in spacetime vertically. Therefore, according to the object, it is not moving in the x direction but only moving in the c𝜏 direction. This means that the constant c, which is the speed of light, is actually a conversion factor of time. The separation in four-dimensions, ds, is just the duration d𝜏 carrying by a clock of a moving observer times the speed of light c. Since each point in this spacetime has a time coordinate and a spatial coordinate, they are called events. This concept is crucial in relativity because it allows us to consider events in both space and time simultaneously, which is necessary for understanding the behavior of objects that are moving at high speeds.

[@mehdizangiabadi-iw6tn]

How is the mass of a black hole measured?

[@chinmayadhiman3358]

Samjha nai jyaada, but sunne me maja aaya😲

[@georgelopera6290]

Please make the equation easier, my head is aching!

[@kingkiller1451]

10:02 I disagree on the basis that I understood it as a nod to the initial prediction of black holes, which was the Schwarzschild Metric, rather than to the later math trying to describe a less idealistic version of the same object. Just my own understanding and opinion though. Otherwise love the video though.

[@Spontaneouscomp]

Can you explain how this spacetime curvature makes things fall when released from rest? (and this is applicable to point particles since they also fall in), so can you explain it via considering the thing as electron in this curvature.

[@aldineisampaio]

According to Nick Lucid, things fall because the time curvature puts their future at a diferent place on space. He explains it beatifully on this video: kzbin.info/www/bejne/a3mueWSQn6yoqqM

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@MaesterSilva]

can't we change the point of view of the 3d pitagoras theoriam and go back to the 2d one? because in practice when you calculate it you do this you get the hipotenuse of the x and y and used it with z. so can't we calculate the 4d one as a 3d one? or turn it into a 2d one?

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@MaesterSilva]

@@Igdrazil I was just theorizing... I don' t study physics for real. I just do for fun. So I like to have theorys and see if they are right or wrong.

[@Igdrazil]

@@MaesterSilva Well it's then fair to say that you completely failed and missed your goal, since you didn't even noticed that the "theory" you were "checking" was DRASTICALLY WRONG SINCE THE BEGINING! You have been "checking" indeed (without any serious fact checking) a FALSE metric, that is neighther Einstein original one (of 18-25 November 1915 on Mercury perihelion), neigther Schwarzschild's one (used in his very first critical letter sent to Einstein in 22 December 1915, nor in his two following fundamental articles of 1916). And that is moreover a very snicky FRAUDULENT one, ARTIFICIALY SINGULAR AND NEGATIVE, whereas Schwarschild one is NON SINGULAR and POSITIVE (of signature (+ - - - ). The signature DOES CRUCIALY MATERS, contrarily as what you fasly pretend since the s is in GR the PROPER TIME (at a factor of light speed which is usualy brought to 1 by adapted choice of units. Otherwise : s=cT where T is the "tau" proper time mesured by a clock attached to the concerned moving "object"). So s is REAL and POSITIVE. Moreover ds is also REAL, and furthemore POSITIVE to respect the obvious ARROW of "time passing". So no way can one takes the farudulent "Hilbert" metric with signature (- + + +) since it gives for a fixed object in his own reference frame (dr=dtheta=dphi=0), a NEGATIVE SQUARED PROPER TIME, thus an IMAGINARY PROPER TIME. This is total NON SENS! It's ok to use so called imaginary "time" like mathematicians like to use to get back formaly to 4D euclidian formal metric like Hilbert did imitating Poincaré of 1900-1905, but then all the interpretations of every letters has to be acorded to this physicaly awkward way of writing things. It's the same problem treated with different maps, but then the letters don't mean the same physical entities and this has to be very clearly explicitaly writen down in a non ambiguous maner so not to create any sniky confusions. The simplest way to write things correctly in a straightforward physical meaningful sens is to keep s and ds REAL and POSITIVE. The "curvilinear length" being (at the scale factor explicit or implicit c), the PROPER TIME of a COMOBILE CLOCK. And in this framework net and clear, the schwarzschild metric is then of signature (+ - - -). Which is the opposit of all those fraudulent metrics that are now used all over in nowdays crazy world of "theoretical physics" that has become a zoo of madness. Moreover the true authentic schwarzschild metric uses R = (r^3+alpha^3)^(1/3) AND NOT r, like ALL sniky fraudulent text book and mad black hole sect write it perversly to make appear ARTIFICIALY "black hole singularity" where THERE IS NONE IN SCHWARZSCHILD METRIC. This is the XXI th century FRAUD. It's a major SCANDAL! Check Schwarschild original papers to see by yourself that in the ds2 you have : gtt =+(1-alpha/R) gRR = - 1/(1-alpha/R) gthetatheta = - R^2 gphiphi = - R^2sin(theta) where R = (r^3+alpha^3)^(1/3) RUNNING FROM the real positive physical SCHWARZSCHILD RADIUS alpha=2GM/c^2, to + infinity. Thus there is NO SINGULARITY since R converges to alpha when r converges to zero. The parameter r being mathematicaly r=sqrt(x^2+y^2+z^2), but who DO NOT REPRESENT A PHYSICAL DISTANCE ON THE PSEUDO RIEMANIAN MANIFOLD. This r is thus simply a mathematical parameter, NOT A PHYSICAL DISTANCE, NOT A PHYSICAL RADIUS. So please stop feeding this spreding XXIth century religion of lies that is replacing Science at the speed of light. We need the Truth and Science to be courageously protected from a potentially deadfull threat. It's only 3 hundred years that it emerged from dogmatic dictature of global lies and non sens. It's fragile and it's massively attacked, within the very institutions that should protect it the most. Check Vankov peer review brilliant article that makes all this cristal clear : www.researchgate.net/publication/342530884_Einstein%27s_Paper_Explanation_of_the_Perihelion_Motion_of_Mercury_from_General_Relativity_Theory

[@rafaelgarciamoheno4938]

great video! Im wondering, does this equation change when talking about the mathematical concept of white holes?

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R

[@_John_Sean_Walker]

In the equation at the beginning of the video, you can also divide both sides by d.

[@Kumar-oe9jm]

No u can't.If u took calculus, u would know what it means.

[@_John_Sean_Walker]

I was joking. But it is a well known shortcoming in physics. We ran out of letters. Little 'm' cancels out all the time. 😂

[@jojothefrikkenclown]

Please just put all relevant equations in the description with comments so we can just dive in on our own time.

[@omekafalconburn9202]

Cool videos, I not convinced on stars not having charge it seems that stars and whole galaxies are linked by plasma filaments with massive magnetic fields, would be good if you could have a look at the physics of electric currents in a plasma ie cosmic z- pinch

[@Igdrazil]

Bullshit THIS IS NOT SCHWARZSCHILD METRIC. This one is a fraud artificialy SINGULAR, whereas the true Schwarzschild 1915-1916 metric is crucialy NON SINGULAR..And Schwarzschild insists very clearly on that. Indeed Schwarzschild in perpouse, does NOT use r, but R instead, which is defined by R=(r^3 + a^3)^{1/3}. So everywhere you illigitimatly use r in your false "Schwarzschild metric", Schwarzschild himself uses R! Soooooooo R MUST ALWAYS BE GREATER OR EQUAL TO a. And this changes everything because when the radial purely mathematical (NOT PHYSICAL !) "distance" r=sqrt(x^2+y^2+z^2) converges to zero, the PHYSICAL R of Schwarzschild metric converges toward a, where this a is thus the INCOMPRESSIBLE PHYSICAL RADIUS OF SCHWARZSCHILD SPHERE. It makes no sens to go beyond a. The region R