Time dilation?

[Douglas]

I'm not really seeing the logic there. "Causally disconnected" happens because the light cones of anything inside the horizon point toward the singularity, so there's no future in which you can somehow get out. It's not some sort of mystical field that disconnects everything higher up from everything lower down, it's an either-or thing--either you're doomed to fall into the centre, or you're not.

It's not even that, really, it's more that the basic principle of relativity still applies. If your blood is inside the event horizon, it's true that it can't go outward. It can, however, go inward less quickly than your arteries do, which would work out the same as far as your internal biology is concerned.

[BaronOfHell]

From what I understand (and looking at the post right above me, I might be woefully out of my depth here), time slows down as you approach the horizon, and becomes infinite at the horizon.

But if it actually goes to infinite, how can you "Cross" the horizon and wind up inside? At least, it seems to me that you'd actually wait just outside the horizon until the BH evaporates over "forever".

To continue on this tangent, if it's alright, something I wonder about is if the gravity from an object formed as a flat ring is the same at all points outside the ring as it would be for all points outside a massive disk of the same mass?

If so, wouldn't there be nothing inside a black hole?

If not, how did "the dragons" get inside the hole (from our perspective) if it requires infinite time from our perspective for this to happen?

And when a black hole increases in size (radius and mass), does the density of the matter at the disk increase as more stuff is pushed into a larger circumference away from the black hole center, or does stuff somehow fall beyond the event horizon as the event horizon is pushed further away from the center of the black hole due to the increase in mass?

[gomipile]

To continue on this tangent, if it's alright, something I wonder about is if the gravity from an object formed as a flat ring is the same at all points outside the ring as it would be for all points outside a massive disk of the same mass?

This seems like a Newtonian question. The answer (in Newtonian physics) is no. Rings and discs produce different gravitational fields. Deriving a similar result for general relativity with enough mass to make it clearly non-Newtonian would be pretty difficult, and I don't know what the result would look like.

If so, wouldn't there be nothing inside a black hole?

I feel like you left out some reasoning after your question and before this. I have no idea what you think the connection could be between rings and discs and black holes.

[BaronOfHell]

Thank you for your reply.

My thoughts were that since nothing can ever pass the event horizon (from our perspective), all the mass of the black hole might be at the event horizon.
Then I imagined a black hole as a ring and wondered if it would be possible based on the gravitational pull from a black hole to determine if it is a ring or a disk.

After asking the question I later speculated that my assumption of a black hole being either a disk or a ring could be incorrect, which I take from your reply to be the case (that it was an incorrect assumption).

[Bohandas]

I'm having a problem thinking about time dilation in relation to black holes.

The gravitation at the event horizon of black holes is variable. Time dilation at black holes is due to the gravitational field, however it is assumed that it approaches infinity as it approaches the event horizon, even though the gravity at the event horizon is variable.

It becomes infinitely concentrated at the singularity, not the event horizon. The event horizon has a variable distance from this depending solely on how much matter ypu're infinitely compressing

[Anymage]

It's not even that, really, it's more that the basic principle of relativity still applies. If your blood is inside the event horizon, it's true that it can't go outward. It can, however, go inward less quickly than your arteries do, which would work out the same as far as your internal biology is concerned.

Fair. That solves the immediate question, and I'm sure that others boil down to nobody knowing the exact details because they're untestable.

To continue on this tangent, if it's alright, something I wonder about is if the gravity from an object formed as a flat ring is the same at all points outside the ring as it would be for all points outside a massive disk of the same mass?

If so, wouldn't there be nothing inside a black hole?

If not, how did "the dragons" get inside the hole (from our perspective) if it requires infinite time from our perspective for this to happen?

And when a black hole increases in size (radius and mass), does the density of the matter at the disk increase as more stuff is pushed into a larger circumference away from the black hole center, or does stuff somehow fall beyond the event horizon as the event horizon is pushed further away from the center of the black hole due to the increase in mass?

Moving up from 2D versions to 3D, it's basic high school physics that a spherical shell can be treated as a point mass at the center for anybody outside, and is gravitationally null for anybody inside. Since falling inside means crossing the horizon yourself and all that entails, for a very basic approximation you could treat it as a big spherical shell.

There are relativistic and quantum effects that happen nearby that may or may not be compatible with treating it as the empty spherical shell model, I wouldn't even know where to begin checking those.

[halfeye]

I'll give your question a qualified "no," because I answered it in more nuanced detail up-thread.

I didn't understand that answer or notice the nuance, sorry.

Your asking that question in response to the part of mine you just quoted is a non-sequitur, though. I'm just saying that your use of the inverse square law specifically, and your continued use of Newtonian intuition in general is useless for general relativity problems.

It's all I have to use *shrug*, if I don't understand something, I don't/can't remember it.

Let's step back a second.

There's a type of black hole, called a schwarzchild black hole, that comes from the same place as the frictionless planes and point masses you see in physics exams. It isn't rotating, isn't charged, isn't near any other significant sources of gravity, and is basically idealized to help you get the basics down. For these you can approximate them, at least from the outside, by assuming a newtonian point mass in the center and everything inside the event horizon is "here there be dragons". Gravity at the event horizon of a schwarzchild black hole is the same no matter the size, because the event horizon is defined by a certain gravitational strength.

@gomipile: So, if my previous question was limited to Schwarzchild black holes, would that change your reply?

I appreciate that they probably don't actually exist, but supposing they did, would the gravity at the event horizon be constant despite changes in mass/volume/density?

[gomipile]

@gomipile: So, if my previous question was limited to Schwarzchild black holes, would that change your reply?

No. The Schwarzschild metric is still full-on general relativity. It's just one of the simplest cases. The Schwarzschild solution predicts precession of the perihelion of Mercury, for instance. So it still has curved, non-Euclidean space.

The Schwarzschild solution is the general relativity version of a point mass. It's what you get from Einstein's equation if you just account for a point mass, with no angular momentum or anything else.


Basically, the equivalent in Newtonian gravity would be calculating the orbit of a satellite as though the Earth was a simple point mass. In the real world you see effects from the rotation of the Earth, local variations in the Earth's gravity, the Moon and Sun, etc. But you're still using full-on Newtonian physics for calculating the motion of the satellite. Likewise, the Schwarzschild solution still uses the full field equations of general relativity, it just has fewer initial conditions than other, more complex solutions.

[Devils_Advocate]

So if the gravity at the photon sphere varies, the gravity at the event horizon does too.

I.e. (by modus tollens), if the gravity at the event horizon doesn't vary, the gravity at the photon sphere doesn't either.

And I would expect the gravitational attraction towards the black hole to be the same everywhere on the photon sphere, if every point on the photon sphere is equidistant from the black hole's center of mass, which I assume to be the case. Just like I would expect the force of gravity to be the same everywhere on the event horizon, if every point on it is also the same distance from the black hole's center of mass. (That is to say, the same distance from the center of mass as every other point on the event horizon. Not the same distance from the center of mass as the points on the photon sphere. That's clear, right?)

With all of the relevant caveats that we're talking about an idealized case.

So it's still not clear where you think the problem is.

Do you think that some explanation of how something works is incompatible with some other explanation of how something works? If so, could you tell us which explanations you think contradict each other, and how?

[gomipile]

I.e. (by modus tollens), if the gravity at the event horizon doesn't vary, the gravity at the photon sphere doesn't either.

And I would expect the gravitational attraction towards the black hole to be the same everywhere on the photon sphere, if every point on the photon sphere is equidistant from the black hole's center of mass, which I assume to be the case. Just like I would expect the force of gravity to be the same everywhere on the event horizon, if every point on it is also the same distance from the black hole's center of mass. (That is to say, the same distance from the center of mass as every other point on the event horizon. Not the same distance from the center of mass as the points on the photon sphere. That's clear, right?)

With all of the relevant caveats that we're talking about an idealized case.

So it's still not clear where you think the problem is.

Do you think that some explanation of how something works is incompatible with some other explanation of how something works? If so, could you tell us which explanations you think contradict each other, and how?

Halfeye has been using that phrase structure to mean "varies with the mass of the black hole" not "varies with position around a black hole of a given constant mass."

[halfeye]

I.e. (by modus tollens), if the gravity at the event horizon doesn't vary, the gravity at the photon sphere doesn't either.

I did prove that the gravity at the photon sphere varies with the mass of the black hole. That's why I'm not getting the gravity at the event horizon being constant despite the variation in masses of various black holes.

And I would expect the gravitational attraction towards the black hole to be the same everywhere on the photon sphere, if every point on the photon sphere is equidistant from the black hole's center of mass, which I assume to be the case. Just like I would expect the force of gravity to be the same everywhere on the event horizon, if every point on it is also the same distance from the black hole's center of mass. (That is to say, the same distance from the center of mass as every other point on the event horizon. Not the same distance from the center of mass as the points on the photon sphere. That's clear, right?)

Any particular schwartchild black hole's photon sphere has a uniform radius yes. Different photon spheres have radii that will be different if the masses of the respective black holes are different.

With all of the relevant caveats that we're talking about an idealized case.

So it's still not clear where you think the problem is.

Do you think that some explanation of how something works is incompatible with some other explanation of how something works? If so, could you tell us which explanations you think contradict each other, and how?

Right, troll, I forgot for a minute. Thanks for resurrecting the thread before it died.

[Douglas]

I did prove that the gravity at the photon sphere varies with the mass of the black hole. That's why I'm not getting the gravity at the event horizon being constant despite the variation in masses of various black holes.

Yes, gravity at the photon sphere varies with the black hole's mass, and yes the ratio of the photon sphere's radius and the event horizon's radius is constant. And yes, if inverse square held universally true, that would imply that gravity at the event horizon varies with the black hole's mass.

However, inverse square is an approximation. For most objects, even up to stellar masses, it is a very very good approximation, but it is still an approximation. Close to a black hole is the one major area where it's a bad approximation. At the event horizon itself, inverse square outright breaks and is completely wrong.