Is there anything inside a black hole?

[Green dwarf]

TL;DR

By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it. From an outside perspective, there shouldn't be anything inside a black hole. Everything should be just outside the event horizon.

By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it. From an outside perspective, there shouldn't be anything inside a black hole. Everything should be just outside the event horizon. There shouldn't be a singularity.

 

[martinbn]

This is often said in popular texts, but it makes no sense! What do you mean by say this

By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it.

How does a clock far away make things slow down near the black hole?!!!!

 

[PeroK]

TL;DR: By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it. From an outside perspective, there shouldn't be anything inside a black hole. Everything should be just outside the event horizon.

Reference: https://www.physicsforums.com/forums/astronomy-and-astrophysics.71/post-thread

By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it. From an outside perspective, there shouldn't be anything inside a black hole. Everything should be just outside the event horizon. There shouldn't be a singularity.

There are already a lot of threads on this. The Schwarzschild black hole is an "eternal" black hole, which is a solution to the Einstein Field Equations in vacuum. There is nothing anywhere in that model. There is only spacetime, and all vacuum with a certain spacetime geometry.

We can add a test particle to that model, which falls into the black hole and through the event horizon in finite proper time. Below the event horizon it has a further finite proper time before the model breaks down and the particle literally runs out of time. Note that the "centre" of such a black hole is not a point in space, but more like the end of time. And, "singularity" means where the mathematical model breaks down.

From that point of view, it makes no sense to say there isn't a singularity. The singularity is the (apparent) incompleteness of the mathematical model.

In addition, a star that is sufficiently massive will eventually be unable to resist total gravitational collapse, and forms a stellar black hole. It's true that beyond a certain point in the collapse, light from this process cannot reach a distant observer. Just because a distant observer can never observe an event does not mean that the event does not happen. The first thing to learn in relativity is that space and time are combined into a spacetime continuum; and, that there is no absolute frame of reference in which all things can be described fully. Your clock does not represent absolute time for the whole universe.

What happens to the matter in a collapsing black hole is unclear. The General theory of relativity has a mathematical breakdown and can't be the full story. Again, the singlarity is not a physical point but more like the end of time and represents a theoretical/mathematical (rather than physical) breakdown.

It's hoped that a quantum theory of gravity will more fully explain what happens below the event horizon for a stellar black hole. And that such a theory would be complete and not break down mathematically below the event horizon.

 

[Ibix]

By a clock outside the event horizon, things slow down as they approach the event horizon and never quite reach it.

Just to add to existing answers, this is a (sadly) common misunderstanding. In relativity it turns out that there is considerable flexibility in defining what "at the same time" means for two things that are not in the same place. Some ways of defining it turn out not to assign meaning to "inside the black hole at the same time as something outside", and this includes the simplest definition worked out by Schwarzschild in 1916. Better definitions don't have this issue.

To paraphrase the above, the map is not the territory. That you're using a bad map (Schwarzschild coordinates) that doesn't include the interior of the black hole does not mean the interior does not exist, no matter how many pop sci sources fail to grasp the point.

 

[Green dwarf]

Thank you, @martinbn, @PeroK and @Ibix.

 

[Nugatory]

@Green dwarf did we not go through all of this with you ten years ago? https://www.physicsforums.com/threads/where-is-the-matter-in-a-black-hole.836527/

 

[Neutrin0]

This is often said in popular texts, but it makes no sense! What do you mean by say this

How does a clock far away make things slow down near the black hole?!!!!

Im pretty sure they meant that a clock that’s outside of the event horizon as in near the black hole but not in the event horizon slow down because of gravitational time dilation which was predicted by Einstein. It’s basically time slowing down because of a gravitational source.

 

[Neutrin0]

Im pretty sure they meant that a clock that’s outside of the event horizon as in near the black hole but not in the event horizon slow down because of gravitational time dilation which was predicted by Einstein. It’s basically time slowing down because of a gravitational source.

Also since time is relative I’m assuming they also meant that a clock say on earth would be different than a clock near a black hole because of gravitational time dilation.

 

[Ibix]

It’s basically time slowing down because of a gravitational source.

It's worth noting that this is an over simplification, one which contributes to the confusion around black holes (IMO) by providing a context in which "time stops" sounds like it might be plausible.

A better explanation is that elapsed time for a clock is a measure of "distance" travelled through spacetime, and spacetime curvature close to the black hole allows a clock to take a shorter route through spacetime between two events than a distant clock (and also between pairs of "start" and "stop" events that are deemed simultaneous by Schwarzschild coordinates). The event horizon is the boundary between the region where there are some timelike paths leading back to infinity and the region where the curvature is such that all timelike paths lead to the singularity in finite time. It's a lot less snappy than "time slows down" but it's a lot less likely to lead to the OP's ten-year confusion on the matter.

Note that I put "distance" in scare quotes. Technically the quantity is called interval, and although it is very closely analogous to the familiar concept of distance, the differences between spacetime and space (even a hypothetical 4d space) do lead to some key differences. When talking about elapsed time as a kind of distance measure, though, it's a pretty solid analogy.

 

[martinbn]

Im pretty sure they meant that a clock that’s outside of the event horizon as in near the black hole but not in the event horizon slow down because of gravitational time dilation which was predicted by Einstein. It’s basically time slowing down because of a gravitational source.

The clock near the black hole slows down! Compare to what?

 

[Neutrin0]

The clock near the black hole slows down! Compare to what?

It's worth noting that this is an over simplification, one which contributes to the confusion around black holes (IMO) by providing a context in which "time stops" sounds like it might be plausible.

A better explanation is that elapsed time for a clock is a measure of "distance" travelled through spacetime, and spacetime curvature close to the black hole allows a clock to take a shorter route through spacetime between two events than a distant clock (and also between pairs of "start" and "stop" events that are deemed simultaneous by Schwarzschild coordinates). The event horizon is the boundary between the region where there are some timelike paths leading back to infinity and the region where the curvature is such that all timelike paths lead to the singularity in finite time. It's a lot less snappy than "time slows down" but it's a lot less likely to lead to the OP's ten-year confusion on the matter.

Note that I put "distance" in scare quotes. Technically the quantity is called interval, and although it is very closely analogous to the familiar concept of distance, the differences between spacetime and space (even a hypothetical 4d space) do lead to some key differences. When talking about elapsed time as a kind of distance measure, though, it's a pretty solid analogy.

He re explains it better my definition was over simplified.

 

[javisot]

He re explains it better my definition was over simplified.

What martinbn is trying to point out is that locally, time passes at the same rate at any point in the universe, even near an event horizon. The discrepancy arises when comparing measurements under certain conditions.

 

[timmdeeg]

The clock near the black hole slows down! Compare to what?

Compared to the duration of a far away supernova.

 

[martinbn]

Compared to the duration of a far away supernova.

And how do you compare it to something far way?

 

[timmdeeg]

And how do you compare it to something far way?

The example shows that a far away clock ticks faster compared to a clock close to a black hole.

 

[martinbn]

The example shows that a far away clock ticks faster compared to a clock close to a black hole.

My question is how do you compare clocks that are far away from each other? The answer is that you need a simultaneity convention. Without that it is meaningless.

 

[timmdeeg]

My question is how do you compare clocks that are far away from each other? The answer is that you need a simultaneity convention. Without that it is meaningless.

Yes, agreed.