# Could all matter in a black hole be actually only on its surface (Schwarzschild radius)?

Layman here, sorry if I miss something obvious.

Black hole entropy depends linearly on its surface. If all matter in a black hole would actually be located only on its surface (or very near), wouldn't it cause entropy to behave exactly like that?

My idea is that when new matter falls in a black hole all black hole matter gets displaced further from the center of the black hole. Somewhat akin to how gravitational waves can displace matter far away from black hole. In that way black hole interior is just a (topological) hole in fabric of the space time.

Does this idea violate any known physical laws?

• The absolute truth is that we cannot observe the inside of a black hole. So exactly what is happening on the inside is a mystery. – MaxW Mar 24 '18 at 17:22
• When new matter enters a black hole it experiences time dilation at the event horizon, preventing an external distant observer from seeing any further descent. The black hole gets a little more massive, however, and the schwarzschild radius will go up correspondingly. None of the existing matter moved, but the c of m has been altered. – JMLCarter Mar 24 '18 at 17:38
• So what is the mechanism by which you think all of the matter in a black hole is being displaced by new matter? If it requires time to elapse, then it could well be breaking time dilation. – JMLCarter Mar 24 '18 at 17:40
• @JMLCarter, maybe you don't mean the center of mass, since the center stays at the center (assuming a centrally symmetric black hole). – S. McGrew Mar 24 '18 at 18:09
• Note that the Schwarzschild radius is proportional to the mass. So (at least in 3 dimensions) the surface area, and the entropy, is proportional to $M^2$ -- whereas I would imagine the "amount" of matter to be proportional to $M$. – Siva Mar 24 '18 at 20:59

Black hole entropy depends linearly on its surface. If all matter in a black hole would actually be located only on its surface (or very near), wouldn't it cause entropy to behave exactly like that?

This doesn't really make sense, for a couple of reasons. (1) Once a chunk of matter has fallen into a black hole, we expect the black hole's entropy to remain constant from that time on. Therefore the location of the matter doesn't relate logically to the entropy. (2) In your proposed interpretation, you give no reason why the entropy per unit area should be fixed. In fact, the area of the event horizon is proportional to the square of the amount of matter that has fallen in, so by your interpretation, the entropy should be proportional to the square root of the area.

Another thing you need to realize is that if matter falls into a black hole, it doesn't make sense to discuss where the matter is "now." General relativity doesn't define simultaneity in a way that would make that meaningful. For more on this, see this answer: https://physics.stackexchange.com/a/146852/4552

Somewhat akin to how gravitational waves can displace matter far away from black hole.

Not sure what you mean by this. This sounds wrong.

In that way black hole interior is just a (topological) hole in fabric of the space time.

This is not an interpretation that fits very well with current ideas about relativity. For more details, see this question: Is it possible the space-time manifold itself could stop at a black hole's event horizon? Basically it's the singularity that we describe as a topological hole, not the entire interior.

• @MartinStangel Also, for a static black hole, there is no matter whatsoever anywhere anywhen--this is to say that there is no matter in the story, to begin with! The static uncharged black hole is a solution to the vacuum Einstein equations so the entropy that is assigned to it is really the entropy of the chunk of spacetime itself--this is in consistency with the advanced and successful approaches such as string theory towards explaining the microscopic origin of this entropy as a counting of (roughly) the states of spacetime geometry. – Dvij Mankad Aug 14 '18 at 20:10
• I agree I smuggle in the entropy considering I said black holes are vacuum solutions to Einstein equations--because pure classical black holes have no notion of entropy associated with them. But I think there is no reluctance in accepting that the semi-classical extension of these pure classical black holes also are essentially vacuum solutions--at least that it would be plainly wrong to imagine some matter forming them. Granted that such black holes have the radiation associated with them and the spacetime would not be perfectly vacuum as it is in the case of pure classical black holes. – Dvij Mankad Aug 14 '18 at 20:17

i often get caught up thinking in limited dimensions when approaching a problem like this.

having heard many analogies about this, one that concerns me, and possibly you, is that time slows ('you could watch the end of the universe') or stops near the event horizon.

so occam's razor says; if time stops, does matter move? can it fall into a black hole?

• Re 'you could watch the end of the universe': This is a common misconception—you actually couldn't. See e.g. physics.stackexchange.com/questions/82678/… – balu Aug 18 '18 at 10:18
• As for "if time stops, does matter move?": You're talking about the time in Schwarzschild coordinates, which is usually associated with the time an observer at infinity would see. However, infalling matter does not care about this time coordinate but only about its own proper time. And, contrary to what you're saying, the matter will cross the event horizon in finite proper time, see the link in my previous comment, as well. – balu Aug 18 '18 at 10:30
• i am ever cautious when i hear things like 'time stops' and 'infinite.' i never believed the suggestions i made, knowing that time slows in a gravity well, but does not stop. but balu has pointed me in the direction of some interesting questions and answers, more accurate examples, and other things i will enjoy studying. thanks much for that balu. – chaz327 Aug 19 '18 at 18:06