Do Event Horizons always contain a singularity?

[FallenApple]

So a black hole consists of an event horizon and a singularity in the center.

What about the cosmological horizon( which is also an event horizon)? Is a cosmological horizon's geometric center a singularity?

I can imagine that an electron has a cosmological horizon. Yet an electron is pointlike, with mass/energy, so it somewhat seems like a singularity of sorts.

Even if a cosmological horizon has at it's geometric center empty space, it has energy/momentum/something in it's field, located at that infintesimal point(which is probably a singularity since a point is lower than plank length).

 

[phinds]

So a black hole consists of an event horizon and a singularity in the center.

What about the cosmological horizon( which is also an event horizon)? Is a cosmological horizon's geometric center a singularity?

I can imagine that an electron has a cosmological horizon. Yet an electron is pointlike, with mass/energy, so it somewhat seems like a singularity of sorts.

Even if a cosmological horizon has at it's geometric center empty space, it has energy/momentum/something in it's field, located at that infintesimal point(which is probably a singularity since a point is lower than plank length).

You speak of a "singularity" as though it were a THING. It is not. "Singularity" is just shorthand for "the place where the math breaks down and we don't know WHAT is going on".

 

[Comeback City]

Furthermore, according to Big Bang theory, there is no center to the universe (which I assume is what you are talking about with "cosmological horizon"), no matter what the shape turns out to be (i.e. infinite&flat, finite&curved)

 

[Chalnoth]

So a black hole consists of an event horizon and a singularity in the center.

What about the cosmological horizon( which is also an event horizon)? Is a cosmological horizon's geometric center a singularity?

I can imagine that an electron has a cosmological horizon. Yet an electron is pointlike, with mass/energy, so it somewhat seems like a singularity of sorts.

Even if a cosmological horizon has at it's geometric center empty space, it has energy/momentum/something in it's field, located at that infintesimal point(which is probably a singularity since a point is lower than plank length).

Definitely not. De Sitter space* has an event horizon, but there is no singularity. There is no special point anywhere in De Sitter space (it's uniform everywhere, and the event horizon is relative to a hypothetical observer who could be anywhere and moving at any speed, not a special point in space).

*De Sitter space has a cosmological constant and nothing else, e.g. no matter or radiation.

 

[FallenApple]

Furthermore, according to Big Bang theory, there is no center to the universe (which I assume is what you are talking about with "cosmological horizon"), no matter what the shape turns out to be (i.e. infinite&flat, finite&curved)

I thought everything is the center. Every object has a cosmological horizon from which no information beyond that can reach it due to the expansion of the universe.

 

[FallenApple]

Definitely not. De Sitter space* has an event horizon, but there is no singularity. There is no special point anywhere in De Sitter space (it's uniform everywhere, and the event horizon is relative to a hypothetical observer who could be anywhere and moving at any speed, not a special point in space).

*De Sitter space has a cosmological constant and nothing else, e.g. no matter or radiation.

That reminds me of the regular universe. The universe is expanding everywhere, which means every location can say that there is information somewhere away from it that is redshifted so much that it will never observed.

 

[FallenApple]

You speak of a "singularity" as though it were a THING. It is not. "Singularity" is just shorthand for "the place where the math breaks down and we don't know WHAT is going on".

I realize that it isn't anything concrete. I was just curious if there is this mathematical breakdown at the center of every event horizon.

 

[rootone]

The cosmological horizon is feature of the OBSERVABLE Universe.
If there were a singularity at the center of it, the singularity would be You!, (or another observer)

 

[FallenApple]

The cosmological horizon is feature of the OBSERVABLE Universe.
If there were a singularity at the center of it, the singularity would be You!, (or another observer)

I do have a center of mass, which in theory is either a particle or vaccuum. Either way, when you zoom down, you basically have energy confined in an infintesimal point, making a singularity.

So I could say that my center of mass is a singularity.

 

[Comeback City]

I do have a center of mass, which in theory is either a particle or vaccuum. Either way, when you zoom down, you basically have energy confined in an infintesimal point, making a singularity.

So I could say that my center of mass is a singularity.

Reread what phinds said in post #2 about singularities.

 

[FallenApple]

Reread what phinds said in post #2 about singularities.

I guess that makes sense. So we can't really categorize singularies and see if they have patterns in physics because they don't exist. (unlike 0 or imaginary numbers which at least exist as concepts)

 

[Comeback City]

I guess that makes sense. So we can't really categorize singularies and see if they have patterns in physics because they don't exist. (unlike 0 or imaginary numbers which at least exist as concepts)

I don't think we can say they don't exist at all. We just don't know what they are or how they work.

 

[rootone]

Dividing by zero is a simple kind of singularity.
The result is 'undefined', or alternatively it's any number you like.

 

[PeterDonis]

when you zoom down, you basically have energy confined in an infintesimal point, making a singularity.

No, you don't. Our current models idealize fundamental particles as point particles, but that does not mean they actually are. Experimentally, the best we can say is that their mass/energy is confined within a region about the size of an atomic nucleus (for quarks, anyway--I'm not sure what the current estimate is for leptons, but it's around that same order of magnitude).

 

[FallenApple]

No, you don't. Our current models idealize fundamental particles as point particles, but that does not mean they actually are. Experimentally, the best we can say is that their mass/energy is confined within a region about the size of an atomic nucleus (for quarks, anyway--I'm not sure what the current estimate is for leptons, but it's around that same order of magnitude).

Is it because of the uncertainty principle? Is that why we can say that energy is confined to a finite space?

 

[PeterDonis]

Is it because of the uncertainty principle?

No, because I'm not talking about trying to measure the position and the momentum of the particles (or any other pair of complementary observables). I'm just talking about the fact that our experiments are only able to probe length scales down to about the size of an atomic nucleus. In order to show experimentally that some particle was truly a point particle, we would need to be able to probe down to arbitrarily small length scales.

 

[John Park]

I don't think the rindler horizon is associated with any singularity either.

 

[PeterDonis]

I don't think the rindler horizon is associated with any singularity either.

Good observation; you're correct, it isn't.

 

[Chronos]

Bear in mind the event horizon is an imaginary surface surrounding a compact object where the escape velocity is c. The entire volume inside the EH is a region where the escape velocity should exceed c, which, of course, is forbidden by GR. Thus, it's not just the putative singularity that is undefined, it is the entire volume enveloped by the EH. The singularity is merely the point at which spacetime geometry becomes hopelessly tangled, not an object in any meaningful sense. Presumably quantum gravity is needed to map out the entire undefined region. Good analogies exist in fluid dynamics, where singularities routinely arise. For those interested, Sabine Hossenfelder has commented on this here; http://backreaction.blogspot.com/2009/02/singularities-in-your-kitchen.html.

 

[PeterDonis]

The entire volume inside the EH is a region where the escape velocity should exceed c, which, of course, is forbidden by GR.

No, it isn't. What is forbidden is for any object to locally move outside the light cones. But there are light cones inside the EH, and timelike and null worldlines that move within them. It's just that no such worldlines go from inside the EH to outside the EH.

it's not just the putative singularity that is undefined, it is the entire volume enveloped by the EH

This is not correct. The mathematical model of classical GR is well-defined for any $r > 0$, i.e., all the way to the singularity. For where the model might stop making accurate physical predictions, see below; but in any case, "no longer makes good predictions" is not at all the same as "undefined".

Presumably quantum gravity is needed to map out the entire undefined region.

Some physicists are of the opinion that quantum gravity effects are significant even at the EH, but I don't think it's a mainstream opinion. The whole question of where classical GR will actually break down is an open question for research. One possibility is that it will work just fine all the way down to the Planck scale, which would mean until spacetime curvature becomes of the order of the inverse Planck length squared. For any black hole of stellar mass or larger, this is far inside the EH and close to the singularity.

 

[Chronos]

I expected objections based on something like Gullstrand-Painleve coordinates to resolve FTL issues inside the EH. But, of course, the results of any experiment to validate a coordinate transformation solution could never be communicated external to the EH, so my presumption something like QG is needed to map the entire region inside the EH is not refuted. My intent was to emphasize the fact the EH, not the singularity, marks the point at which our knowledge of physics becomes unreliable.

 

[PeterDonis]

My intent was to emphasize the fact the EH, not the singularity, marks the point at which our knowledge of physics becomes unreliable.

But I don't think that's true either--or at least, it depends on a meaning for "unreliable" that I don't think is very useful. After all, if we are going to take the position that we can never confirm GR's predictions inside an EH, that goes for any putative theory of quantum gravity as well. So your presumption that we need QG to correctly model the EH could never be confirmed--nor could a counterclaim that classical GR works just fine all the way down to one Planck length from the singularity ever be refuted. That doesn't seem like a useful way to proceed.

In other words, if we can never actually get observations from inside an EH, any determination of what theory validly models the interior of a black hole must be made indirectly. And indirectly, we have strong arguments for why classical GR should be valid well inside the EH of a black hole of stellar mass or larger. If we are going to try to justify the position that QG is needed everywhere inside the EH, it won't be because we can't confirm GR's validity there directly; it will be because we have figured out a theory of QG that gives us even stronger arguments for why classical GR should break down at the EH (or even outside it--some QG speculations have been made that seem to indicate that classical GR should break down in some portions of spacetime outside an EH in order to have a sensible model of an evaporating BH). But any such argument for why QG should be reliable inside the EH will be indirect, just as our current arguments for why classical GR should be reliable well inside the EH are indirect.

 

[PeterDonis]

I expected objections based on something like Gullstrand-Painleve coordinates to resolve FTL issues inside the EH.

There are no "FTL issues" inside the EH. Spacetime there, in the classical GR model, has perfectly well-defined light cones and causal structure. That is an invariant statement, independent of any choice of coordinates.

I post this separately since it is a separate issue from the issue of how we can apply any theory at all inside the EH.

 

[rootone]

So a black hole consists of an event horizon and a singularity in the center.

The horizon is what is what an observer observes, and beyond that is not observable.
A singularity at the center of the black hole means that we don't know what is going on beyond the horizon.

 

[PeterDonis]

The horizon is what is what an observer observes

Actually, an observer outside the horizon can't see the horizon itself (as well as anything inside it).

A singularity at the center of the black hole means that we don't know what is going on beyond the horizon.

No, it doesn't. The inability of an observer outside the horizon to see the horizon or what's inside it is a property of the horizon, not the singularity.

 

[rootone]

The inability of an observer outside the horizon to see the horizon or what's inside it is a property of the horizon, not the singularity.

I won't argue with that