For me the truly amazing thing is that Schwarzschild came up with this while he was a gunnery officer in the German army fighting on the Eastern front in WW1. Can you imagine the cold, the danger, the fierce military discipline, the complete absence of any intellectual resources, and still he came up with this extraordinary, ground-breaking idea?
@SnowSalt-u7x we literally love all of these topics!! It will be a pleasure! Thanks for letting us know. We will add them to our list of ideas right now 😎
The Schwarzschild solution always fascinated me because it connects math and physics so beautifully. I remember struggling to grasp the concept of spacetime curvature in high school, but once I saw how the equations worked, it was like seeing the universe through a new lens. Videos like this are a great way to bridge those gaps and make abstract math more tangible. And with platforms like SolutionInn, revisiting these concepts with fresh learning tools can make the journey even more enjoyable.
To understand what you guys just expaliked what are the pre requisite as in an a undergrad in electrical engineering am supposed to be good what topics to understand this ? Thank You.
@@josephsmth646 good question. If you know calculus, linear algebra and tensor calculus you are able to understand this video. Of course, if you reeeeeeally want to understand each little thing we talk about you need to know these subjects (plus the ones we showed in the beginning of the video) in depth. We are planning to post more videos about the math related. Probably one of the next videos will be: “The Core of Tensor Calculus” 😎
Tensors, first. They are more or less the step beyond vectors, which you will already know. Christoffel symbols as well. These are kind of a matrix that describes a transformation as one follows a path and makes curvature rigorous. The superscript and subscript notation will be new as well. It more or less means that simple looking einstein equation is shorthand for a system of equations. The rest of it should make sense to an engineer. 👍
Wait, how does algebraic geometry come into general relativity? AG involves varieties as the 'graphs', or set of points from an affine space, that satisfies polynomial equation(s) involving the variable(s) of the affine space... There's very little polynomial-ish about a manifold whose equations can almost never even be in closed form, let alone polynomials.
@@christressler3857 In algebraic geometry, the singularities of GR can be analyzed by “blowing up” the space around them, replacing the singularity with a smooth structure. For example, take the equation of a cone, which has a singularity at the origin (z^2 = x^2 + y^2). This is an algebraic variety in R^3, with a singularity at (x, y, z) = (0, 0, 0). To resolve the singularity, we perform the blow-up. So, new coordinates (u,v) to parameterize the variety near the origin (x = u * z, y = v * z). And (u, v) are homogeneous coordinates on P^1 (a projective line). Substitute in the cone equation: z^2 = x^2 + y^2 => z^2 = (u * z)^2 + (v * z)^2. Divide through by z^2 (assuming z ≠ 0): 1 = u^2 + v^2. This equation describes a circle in the projective plane P^1. The blow-up replaces the singular point (0, 0, 0) with this smooth structure. Let’s say that singularities are always problematic in math, so substituting an “undefined” behavior with a smooth and well-defined structure might be really useful
@@sphakamisozondi yeah, it is. GR is super rich in math. Anyone studying GR, even if only interested in the physics of it, will have to inevitably learn very advanced math
5:17 : “no electrical charge” : this assumption feels a little odd to to include to me, like, yeah if we are talking about the different types of possible black hole, then 0 electric charge is a requirement to get a Schwartzchild solution, but if we are just talking about plain GR, then I wouldn’t expect this to even come up? Separate topic : is R = R_{\mu, u} g^{\mu, u} ? 5:38 : “distances angles and Casual structures” : you mean distances, angles, and *causal* structure 6:18 : huh, interesting. What’s a(t) here? Also, wait, shouldn’t any metric tensor be consistent with *some* stress energy tensor (or whatever the tensor T was called) ? 7:10 : oh, well that answers my question about R. Glad I remembered that part correctly. Now, if I could remember how the \Gamma tensor worked.. \Gamma is for… well, it’s the connection, right? Uhh… for taking covariant derivatives or something like that? How did it work..? 7:14 : oh, there’s that answered, cool, thanks Well, the name for them (the Christoffel symbol) and the expression for them, though not the meaning of them 7:20 : ah, and confirmed the name of T, thanks Ok, \Gamma_{\mu, u}^\lambda is symmetric in \mu, u iff g_{\mu, u} is.. does g tend to be even when not diagonal? (Is it always?) Edit: oh, I should probably check out the pdf
Oh, not going to mention that the singularity at the Schwartzchild radius is only a coordinate singularity? Also, didn’t the idea of a black hole precede GR by just considering a body where the escape velocity exceeded c ?
Prior to GR c was assumed to be relative to space somehow, so travelling at any speed was possible and black holes were not considered a thing. SR and GR are the natural consequence of c being constant.
1:10 “I know, it is a lot.” Me, already thinking: “Now what if a 4-D rendered simulation on the GPU.” (As a programmer I would like to see the sort of ‘advertising’. department be to create renders of unique edge cases in GR. It has held up shockingly well. Plus, I swear somewhere in these solutions is the safs warping of space time for FTL propagation. Is it a guess? Yeah, totally. But I just think there is something beautiful of this admixture of fields and applied real world phenomena)
@@levinskikirsten Hi so, I assume your description is not in the original English but is in your language, translated by UA-cam automatically. Unfortunately when it does that for some languages it doesn’t translate the link, and it disappears (I know, very weird), so I’ll give it to you here: www.dropbox.com/t/sKrwKqE0tTJNGTKa Next time we’ll pin it in the comments too so it’s easier to find in cases like this :) thanks!
I've had a question about this topic for years that hasn't been answered yet. Does Schwarzschild's solution to the radius of black holes depend on the distance of the observer? And was the viewer placed at a point infinitely far away? To get a simple solution? Because the observer can fly into the gravitational field. And have a finite distance from the black hole. From my intuitive point of view, the observer should be able to see further and further behind the event horizon of the black hole. Until it dissipates when the observer arrives at the center of the black hole. For spaceships there is escape velocity. But if you want e.g. For example, if you only go up from Earth into an orbit at a height of 500 km, the speed is lower. Shouldn't one also calculate the Schwarzschild radius depending on the distance of the observer from the black hole?
The answer to your first question is found in the video: the Schwarzschild radius R is given by R = 2MG/c^2. Do you see any dependence on observer parameters in this expression? No? So, the Schwarzschild radius does NOT depend on the observer. The answer to your second and third questions is NO.
@@User-jr7vf Yes. But this is the final solution. Under what condition was it calculated? And the Schwarzschild radius is abrupt. What physicists have problems with.
It depends on a coordinate system outside the event horizon, that is true. In this coordinate system the entire horizon is one point and it appears to take forever to cross said horizon because the slope of the curvature is vertical, which is to say infinite. Penrose coordinates behave differently, and cause a swap between time and space at the horizon. An observer there would not bump into a wall or anything though. Which one is accurate? They both are.
Hi so, I assume your description is not in the original English but is in your language, translated by UA-cam automatically. Unfortunately when it does that for some languages it doesn’t translate the link, and it disappears (I know, very weird), so I’ll give it to you here: www.dropbox.com/t/sKrwKqE0tTJNGTKa Next time we’ll pin it in the comments too so it’s easier to find in cases like this :) thanks!
Useless, since we don't understand what a black hole is. Schwartzschild's solution for a theoretical non existent object. . By the way wha't the math for Mercury's orbital ?
Automatic translation is something you can turn off in your own settings in your device. It’s something youtube does automatically whenever your device’s language is not english :) It’s not something we set for titles and description, so not up to us.
Too bad it is not explained what happens at the Schwarzschild radius....... Which by the way is a true singularity, as a result of which black holes simply don't exist.
PDF link if you want a more detailed explanation:
drive.google.com/file/d/17dpI_Y4zBkMwlze85L1ITcnbBtRzBYHq/view?usp=sharing
For me the truly amazing thing is that Schwarzschild came up with this while he was a gunnery officer in the German army fighting on the Eastern front in WW1. Can you imagine the cold, the danger, the fierce military discipline, the complete absence of any intellectual resources, and still he came up with this extraordinary, ground-breaking idea?
@@waylandsmith8666 oh yeah!! It is true! Honestly, it shows me that we have no excuses
Schwarzschield came up with his solutions during one night in a trench at the eastern front. The guy was a genius.
@@70mavgr yeah, it is really incredible. I don’t know how he could keep his focus under so much pressure and stress
@SnowSalt-u7x we literally love all of these topics!! It will be a pleasure! Thanks for letting us know. We will add them to our list of ideas right now 😎
smoked too much weed , why the heck is yt recommending me this stuff i don't even understand
That’s an awesome way to start learning math 🍄🟫🍀
Weed has a way of making math/physics seem even more astonigshly existentially profound that it already is.
@@dibeos What animation software do you guys use may I ask since everything is really pretty!
@@dibeosojala lo doblen al español 😢
@ we just use keynotes :)
Cool idea to talk about physics to bring mathematical concepts to life
The Schwarzschild solution always fascinated me because it connects math and physics so beautifully. I remember struggling to grasp the concept of spacetime curvature in high school, but once I saw how the equations worked, it was like seeing the universe through a new lens. Videos like this are a great way to bridge those gaps and make abstract math more tangible. And with platforms like SolutionInn, revisiting these concepts with fresh learning tools can make the journey even more enjoyable.
@@Blingsss we are glad to know that you enjoyed the video. We are planning many more videos where we will show bridges between math and physics 😎
Man!!! The quality!!! Remember us when you get big
@@asifalamgir5135 😂😂😂 We will only remember Asif
i really like this channel, thanks for your work
To understand what you guys just expaliked what are the pre requisite as in an a undergrad in electrical engineering am supposed to be good what topics to understand this ? Thank You.
@@josephsmth646 good question. If you know calculus, linear algebra and tensor calculus you are able to understand this video. Of course, if you reeeeeeally want to understand each little thing we talk about you need to know these subjects (plus the ones we showed in the beginning of the video) in depth. We are planning to post more videos about the math related. Probably one of the next videos will be: “The Core of Tensor Calculus” 😎
Tensors, first. They are more or less the step beyond vectors, which you will already know.
Christoffel symbols as well. These are kind of a matrix that describes a transformation as one follows a path and makes curvature rigorous.
The superscript and subscript notation will be new as well. It more or less means that simple looking einstein equation is shorthand for a system of equations.
The rest of it should make sense to an engineer.
👍
THANK YOU GUYS I LOVE YOU ALL
we love you more 😎
awesome video, really like it thanks for your work
@@entertainmentupdates5730 thank you for the nice comment!! And please let us know what kind of videos you’d like to see in the channel 😎
Wait, how does algebraic geometry come into general relativity? AG involves varieties as the 'graphs', or set of points from an affine space, that satisfies polynomial equation(s) involving the variable(s) of the affine space... There's very little polynomial-ish about a manifold whose equations can almost never even be in closed form, let alone polynomials.
OK sure, SO(3) I can see coming from alg. geo....
@@christressler3857 In algebraic geometry, the singularities of GR can be analyzed by “blowing up” the space around them, replacing the singularity with a smooth structure. For example, take the equation of a cone, which has a singularity at the origin (z^2 = x^2 + y^2). This is an algebraic variety in R^3, with a singularity at (x, y, z) = (0, 0, 0). To resolve the singularity, we perform the blow-up. So, new coordinates (u,v) to parameterize the variety near the origin (x = u * z, y = v * z). And (u, v) are homogeneous coordinates on P^1 (a projective line). Substitute in the cone equation:
z^2 = x^2 + y^2 => z^2 = (u * z)^2 + (v * z)^2.
Divide through by z^2 (assuming z ≠ 0):
1 = u^2 + v^2.
This equation describes a circle in the projective plane P^1. The blow-up replaces the singular point (0, 0, 0) with this smooth structure.
Let’s say that singularities are always problematic in math, so substituting an “undefined” behavior with a smooth and well-defined structure might be really useful
@dibeos sure, but can blowing up be lifted from varieties to arbitrary manifolds like this? Or are the techniques that accomplish this, different?
No wonder Einstein took him some time to come up with GR 😲. From Tensor Calculus to Topology, damn that's a lot
@@sphakamisozondi yeah, it is. GR is super rich in math. Anyone studying GR, even if only interested in the physics of it, will have to inevitably learn very advanced math
5:17 : “no electrical charge” : this assumption feels a little odd to to include to me, like,
yeah if we are talking about the different types of possible black hole, then 0 electric charge is a requirement to get a Schwartzchild solution,
but if we are just talking about plain GR, then I wouldn’t expect this to even come up?
Separate topic : is R = R_{\mu,
u} g^{\mu,
u} ?
5:38 : “distances angles and Casual structures” : you mean distances, angles, and *causal* structure
6:18 : huh, interesting. What’s a(t) here?
Also, wait, shouldn’t any metric tensor be consistent with *some* stress energy tensor (or whatever the tensor T was called) ?
7:10 : oh, well that answers my question about R. Glad I remembered that part correctly.
Now, if I could remember how the \Gamma tensor worked..
\Gamma is for… well, it’s the connection, right? Uhh…
for taking covariant derivatives or something like that?
How did it work..?
7:14 : oh, there’s that answered, cool, thanks
Well, the name for them (the Christoffel symbol) and the expression for them,
though not the meaning of them
7:20 : ah, and confirmed the name of T, thanks
Ok, \Gamma_{\mu,
u}^\lambda is symmetric in \mu,
u iff g_{\mu,
u} is.. does g tend to be even when not diagonal? (Is it always?)
Edit: oh, I should probably check out the pdf
Oh, not going to mention that the singularity at the Schwartzchild radius is only a coordinate singularity?
Also, didn’t the idea of a black hole precede GR by just considering a body where the escape velocity exceeded c ?
Prior to GR c was assumed to be relative to space somehow, so travelling at any speed was possible and black holes were not considered a thing. SR and GR are the natural consequence of c being constant.
4:26 is it same as co moving coordinates
1:10 “I know, it is a lot.”
Me, already thinking: “Now what if a 4-D rendered simulation on the GPU.”
(As a programmer I would like to see the sort of ‘advertising’. department be to create renders of unique edge cases in GR. It has held up shockingly well. Plus, I swear somewhere in these solutions is the safs warping of space time for FTL propagation. Is it a guess? Yeah, totally. But I just think there is something beautiful of this admixture of fields and applied real world phenomena)
Where's the PDF below?
in the description the first link
@@levinskikirsten Hi Eric, did you find it?
@@dibeos there's only amz, vpn, social media and patreon.
@@levinskikirsten Hi so, I assume your description is not in the original English but is in your language, translated by UA-cam automatically. Unfortunately when it does that for some languages it doesn’t translate the link, and it disappears (I know, very weird), so I’ll give it to you here: www.dropbox.com/t/sKrwKqE0tTJNGTKa
Next time we’ll pin it in the comments too so it’s easier to find in cases like this :) thanks!
@dibeos thank you, I'm from Brazil, that's exactly what happened.
Good 👍
@@chevasit thanks Chevasit 😎
I've had a question about this topic for years that hasn't been answered yet.
Does Schwarzschild's solution to the radius of black holes depend on the distance of the observer? And was the viewer placed at a point infinitely far away? To get a simple solution?
Because the observer can fly into the gravitational field. And have a finite distance from the black hole. From my intuitive point of view, the observer should be able to see further and further behind the event horizon of the black hole. Until it dissipates when the observer arrives at the center of the black hole.
For spaceships there is escape velocity. But if you want e.g. For example, if you only go up from Earth into an orbit at a height of 500 km, the speed is lower.
Shouldn't one also calculate the Schwarzschild radius depending on the distance of the observer from the black hole?
The answer to your first question is found in the video: the Schwarzschild radius R is given by R = 2MG/c^2. Do you see any dependence on observer parameters in this expression? No? So, the Schwarzschild radius does NOT depend on the observer. The answer to your second and third questions is NO.
@@User-jr7vf Yes. But this is the final solution. Under what condition was it calculated? And the Schwarzschild radius is abrupt. What physicists have problems with.
It depends on a coordinate system outside the event horizon, that is true. In this coordinate system the entire horizon is one point and it appears to take forever to cross said horizon because the slope of the curvature is vertical, which is to say infinite.
Penrose coordinates behave differently, and cause a swap between time and space at the horizon. An observer there would not bump into a wall or anything though.
Which one is accurate? They both are.
Sehr gut
Wir freuen uns, dass es Ihnen gefallen hat 😎
nice
there's no link in the bio of the video maybe a mistake?
Hi so, I assume your description is not in the original English but is in your language, translated by UA-cam automatically. Unfortunately when it does that for some languages it doesn’t translate the link, and it disappears (I know, very weird), so I’ll give it to you here: www.dropbox.com/t/sKrwKqE0tTJNGTKa
Next time we’ll pin it in the comments too so it’s easier to find in cases like this :) thanks!
Write in google: singularity sphere in the heart of a black hole
tendi foi nada, amei! 🫰🏽
I subbed to sam sulek when he had 10k subs. Now he has 4M or something. Hopefully this channel does the same. :-)
@@deltalima6703 we are hoping for the same!! but it can’t be done without people like you so thank you ;)
Useless, since we don't understand what a black hole is. Schwartzschild's solution for a theoretical non existent object. . By the way wha't the math for Mercury's orbital ?
Le bouclier de Schwarz 😂😂
You shouldn't use automatic translation, everybody learns english at school.
Automatic translation is something you can turn off in your own settings in your device. It’s something youtube does automatically whenever your device’s language is not english :) It’s not something we set for titles and description, so not up to us.
Too bad it is not explained what happens at the Schwarzschild radius....... Which by the way is a true singularity, as a result of which black holes simply don't exist.
@@peterdamen2161 yeah, we added more details in the pdf link
@@dibeos Not really. You still didn't explain why you think that the singularity at the Schwarzschild radius is not a true singularity.....
just a combinaison of .... , you joker