A story about charged black holes

Here we take a look at the mathematics of charged black holes from a different point of view, by analyzing the Reissner-Nordstrom metric.
Slowmo bouncing ball, creds to Florian Knorn: • Ball bouncing in slow ... thank you
The electromagnetic tensor at 10:35 link • Transforming four Maxw...
References:
Reissner-Nordström metric
en.wikipedia.o...
The Reissner-Nordström metric
www.diva-porta...
Derivation of the Metric of Reissner-Nordstrom¨ and Kerr-Newman Black Holes
idus.us.es/bit...
Music:
pixabay.com/us...
VO:
fliki.ai

[@sarthakasingh2179]

Charged black holes have a little problem, if we take 2 charged blackholes and take out small pieces of the two size of subatomic particles, then to exert electrostatic force on one another there will be an exchange of virtual photons as per Quantum Electrodynamics. But, issue is black hole by definition is a body whose escape velocity is greater than speed of light, hence not even light can escape it. The 2 charged black holes can't exert electrostatic force on anyone.

[@math.101]

That's a very good point ... it's barely suggested at the end of the video, but my guess is that electric charge also creates curvature, but not in the way the Reissner-Nordstrom metric describes. Thank you for taking the time to write this comment, I hope you enjoyed it

[@tridivsharma2342]

this channel is too underrated

[@myu_on]

I love it when videos marry math and astrophysics, the best thing ever! Very underrated, I’m rooting for this channel’s growth 😃

[@staticnullhazard6966]

This topic just crossed my mind. Thank you for making this video. Very interesting and apparently not yet fully understood. Especially 16:42 is kind of mind blowing. So if we see a massive object collapsing, we can simply charge it to prevent the creation of a black hole. Fascinating.

[@math.101]

Hi, I'm glad you enjoyed it, thank you ... apparently you can do that, yes 😊 ... which doesn't look 100% right to my eyes

[@kellymoses8566]

It would NOT be simple to give enough charge to that much mass!

[@pavelrozhkov3239]

I like your ideas, but I don't think that you can equate gravity and electromagnetism. For gravity the main dynamical variable is metric tensor, and for electromagnetism the main dynamical variable is electromagnetic four-potential. One is rank 2 tensor, the other is a rank 1 tensor, and so they have different symmetries and different amount of degrees of freedom.

[@math.101]

Thank you

[@pavelrozhkov3239]

​@@math.101 By the way, there is Kaluza-Klein theory, where gravity and electromagnetism are properly merged into one entity, but it requires additional spatial dimension. Charge is thought as the component of particle's momentum directed in this fifth dimension.

[@math.101]

Yes, physically speaking it's more difficult to make assertions. On the other hand, mathematically speaking, the field has to have a certain structure to solve the differential equations, and both fields do the job. I really should read more about Kaluza-Klein theory, several viewers pointed that out, thanks

[@ZeDlinG67]

Wow, you are getting better and better at this :) Manim makes it look like a 3b1b video, but your algebra autopilot is more reminiscent of Mathologger ;) Can't wait for the next

[@adenwellsmith6908]

1. Take one black hole 2. Shoot electrons at it. 3. What happens when the charge gets so high that you get the naked singularity? My gut feel is that since matter is net electrically neutral the charge is very small, miniscule compared to the actual mass. If you add one charge, say one electron, that adds to the mass, adds to the charge. The ratio of mass to charge then matters to see if you can get a naked singularity. Which has the bigger effect?

[@math.101]

That's a good question, honestly I don't know the answer. My guess is that we shouldn't think about the "electric energy" as stored in the field itself ... I'm glad you enjoyed it, thank you

[@ericgolightly8450]

I've heard it's impossible to create a naked singularity. You can get close, but never exactly there.

[@adenwellsmith6908]

@@ericgolightly8450 No, you will get there. it's people outside of the event horizon that won't see you get there.

[@stayinthepursuit8427]

Can we create (increase) artificial gravity by charging objects shooting them with radiation, if M irr is small enough

[@IndependentPhysics]

Have you considered that the negative potential energy in the interior of your new electric case black hole could counteract the energy of the singularity, leading to a regular interior solution and a usual exterior solution?

[@math.101]

Hey, nope, I haven't ... how would that go?

[@mahmudunnabisiam]

Amazing video. I was pretty good with the first half part of the video and then it got out of my knowledge. LOL. Great video lad. Keep making it.

[@math.101]

Glad you enjoyed it!

[@edd.]

I love this channel. I can’t get the ink to work for the EM tensor

[@math.101]

Hi, I'm glad you like this channel, thanks ... I've done some parts about that video, but my lack of time is huge. Let me provide you an alternative video, this one kzbin.info/www/bejne/gGiQp32oh92FapI

[@RamAdithyaMuthukumarasamy]

Amazing video! Could you make similar videos for the Kerr Newman metric and the kerr metric? It would be really useful

[@math.101]

If I find the time, then yes, absolutely

[@cykkm]

"child" in Schwarzchild is pronounced like "shield". Incidentally, it also means "shield". :)

[@shafaet1995]

It's just blown my mind. Amazing. ❤️❤️

[@math.101]

thanks

[@umairali-ps5ly]

great video

[@math.101]

Thanks!

[@user-hq3dq3vx5x]

At 7:30, the phrasing is very confusing. No, the basis vectors can change from place to place, both in size and direction, even on a flat manifold with Levi-Civita connection. Consider polar coordinates, where the lengths of the basis vectors aren't normed to 1. We can't tell anything about curvature being present or not before calculating the Riemann tensor. To make things even worse, an Euclidean space can appear curved with the right choice of connection, bc. curvature and torsion are dependent on the connection, and not on the metric or the chosen basis, in the most general case. Another thing that will 100% confuse the newcomers is the location of Schwarzschild mass. A Penrose diagram would be more suitable, I think. The mass is not in the 'center', at least not the way a layman would assume. At the 'center', based on your diagram, is an Einstein-Rosen bridge. The (Komar) mass is at the future and past spacelike singularity. An infaller has only causal access to the past/white hole one. The geometric unification of electricity and gravity has a very rich literature, I don't think that you can show anything new in this topic, but hey, who am I to judge/ruin the fun. One approach is that bc. of Noether/local conservation of charge, we have local U(1) gauge invariance (analogous to local Poicaré invariance in GR). The global one comes from the fact, that we only ever measure the absolute value squared of the wave function, and not the function itself. Bc of this, just like basis vectors in GR, the U(1) phase can vary from place to place. This necessitates the gauge covariant derivative/an Ehresmann connection (analogous to the Levi-Civita in GR) in the U(1) principal g-bundle (analogous to the tangent bundle). This is just the electromagnetic four-potential/connection 1-form (analogous to the Christoffel symbols). We can calculate the holonomy/curvature of this by taking the exterior derivative of A_mu, and that will be the Faraday tensor/curvature 2-form (analogous to the Riemann curvature tensor). Another approach is Kaluza-Klein, where you make your spacetime manifold 1+4 D instead of 1+3 D, but compactify the 4th spacial dimension. You incorporate the electromagnetic four potantial into the metric. In this formalism, the Faraday tensor isn't a curvature 2-form, but part of the connection. With this, you get back GR + Maxwell's equations (Lorentz force included) for free. This idea later became string theory. Einstein had a theory in which elementary particles are just geons/solitons of the spacetime manifold itself. There are a few more I know of, like teleparallelism and LQG, and probably many more, that I don't know of.

[@math.101]

Hi, very nice analysis, you are right, the phrasing at 7:30 is confusing, although I also said "we say it's curved depending on the form of the functions" I should've chosen different words yes. And although I later refer to a singularity not being in the future, you are right again about the location of Schwarzschild mass. It's so hard to come up with a good script without messing things up. I'm super glad you took the time to watch it and write this comment, thanks ... I've never dived deep into Kaluza-Klein theory, several viewers pointed that out several times, I hope to find some time to do so ... Lastly, I still think this is not the correct way to describe a charged black hole ... Either we make the same considerations for the gravitational field, or not at all for the electric field ... that discrimination looks arbitrary from a mathematical perspective, this is related to the question I ask around 19:47 ... hey, thanks again, I hope you enjoyed it

[@user-hq3dq3vx5x]

​@@math.101 Yes, about Reissner-Nordström. The thing is, no one takes that solution seriously. Thinking about the unification of forces is very important, but thinking about RN is a waste of time, in my opinion. First of all, this solution can not exist, even in GR, bc. of the Poisson-Israel mass inflation instability at the inner Cauchy horizon (1), it is an eternal metric, real holes are not; they form and evaporate (2), it assumes vacuum and a classical EM field, but in QED the vacuum is not empty, and the force is mediated by virtual photons (3). Fx. Einstein-Cartan theory introduces an antisymmetric stress-energy tensor for spin, and a connection with torsion to handle real particles with spin/the Dirac equation (albeit making it nonlinear). The black hole solutions are very different in EC, they have no singularity. In GR, you can't handle real fermions/spinors. Today, the majority of theoretical physicists think of GR as a low energy, effective field theory approximation of an interacting massless spin 2 gauge boson. TL;DR: GR is very special despite the name, and is a very bad approximation, despite the measurements we can make today.

[@syndicatedpuzzles]

Brilliantly made and voiced video. So what is the relative contribution of charge to mass in observed black holes, or speculated to be? Got to be small as we'd hear about it more in discussions of black holes.

[@farmerinter6791]

You're doing great man

[@kokosensei5231]

Thank you for share!

[@manw3bttcks]

2:11 it would have been more consistent at the attractive case to have the charge signs different instead of both "+"

[@math.101]

Hi, yes, I've considered that, I ended up doing it with the same sign just for animation purposes, thanks for the suggestion, I hope you enjoyed the video

[@GoldyMarko]

10:35 i am sorry but can someone answer to this comment with link to that video please, i can't find it in description....

[@math.101]

Hi, that's a Work In Progress ... I'm gonna upload it soon

[@GoldyMarko]

Hey@@math.101, don't wanna hurry you up or rush, but just curious if you forgot about it :(

[@math.101]

Hi @@GoldyMarko, Instead of feeling rushed, I feel motivated, thanks :) ... I can only spend part of my free time on these videos, so it's far from ideal. Yet, I've got some of the animations and part of the script already done

[@kellymoses8566]

The math of quantum mechanics is simple but its implications are incomprehensible. The implications of General Relativity are comprehensible but the math is incomprehensible.

[@BurkhonAbidkhanov]

Thank you man !!!!

[@math.101]

You're welcome

[@BorisNVM]

really really cool

[@dwoopie]

Your curves are going the wrong way... this way you won't find gravity either... or... Einsteins curves from general...negative curves also ...would never give you gravitation lensing..you only get that is you count positive with special...

[@math.101]

Hi, nice feedback, what would be a better way to visualize it?

[@dwoopie]

@@math.101 make Einsteins equation count positive... special starting at 1 sec for time calculations... and general go positive...to find force (force is a new law of nature together with time) which creates gravity...gravitation lensing...faster than light travel... lots of fun

[@math.101]

I get it, yes, it would be nice to visualize it positively as well