Definition of black hole for the purposes of no-hair theorems?

In summary, the no-hair theorem for general relativity coupled to electromagnetism states that all stationary black hole solutions with a non-degenerate horizon can be described by their mass, angular momentum, and electric charge. The definition of a black hole in this context is a region of spacetime from which it is impossible to escape to future null infinity, known as the event horizon. The concept of asymptotic flatness is used to define this region and exclude certain solutions such as topological defects. Other characterizations of black holes, such as the presence of "hair," are not addressed in this theorem.
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bcrowell
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definition of "black hole" for the purposes of no-hair theorems?

Living Reviews has a nice review article on no-hair theorems: http://www.livingreviews.org/lrr-1998-6 Their rough verbal statement of the no-hair theorem for GR coupled to E&M is: "all stationary black hole solutions to the EM equations (with non-degenerate horizon) are parametrized by their mass, angular momentum and electric charge."

I have a really elementary question, which is how "black hole" is defined in this context. Maybe I'm missing it, but I don't see anywhere in the Living Reviews article where they come out and say this plainly.

It seems to me that it can't be "a black hole is any electrovac solution with a singularity," because then the proof of the no-hair theorem would seem to be a proof of cosmic censorship in the case of GR+EM, which I assume has not been proved...? Is [itex]\Lambda=0[/itex] assumed? For the purposes of this theorem, does "black hole" include things like topological defects? Is it explicitly limited to things that have an event horizon? How about things that aren't asymptotically flat?
 
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Via the event horizon, at least in figure 1. They also give state asymptotically flat.
 
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Thanks for the reply, atyy! So you think the definition is effectively given in the figure? I guess it makes sense that they define it as having an event horizon, since otherwise I guess you'd have to prove cosmic censorship in order to prove a no-hair theorem.
 
  • #4


atyy said:
Via the event horizon, at least in figure 1. They also give state asymptotically flat.

Asymptotic flatness is used to define what "escape to infinity" means.

The standard definition of the black hole region of an asymptotically flat spacetime is the region of spacetime from which it is impossible to escape to future null infinity. An event horizon is the boundary of this region.

The review article Black Hole Boundaries by Ivan Booth,

http://arxiv.org/abs/gr-qc/0508107,

explores other characterizations of black holes, but I don't think thinks that it looks at "hair".
 

1. What is a black hole?

A black hole is a region of space where the gravitational pull is so strong that nothing, not even light, can escape it. This happens when a massive star dies and collapses, creating a singularity with infinite density and zero volume.

2. How is a black hole defined for the purposes of no-hair theorems?

In the context of no-hair theorems, a black hole is defined as a solution to Einstein's field equations that has a horizon, is stationary, and has no hair - meaning it is uniquely described by its mass, charge, and angular momentum.

3. What are no-hair theorems?

No-hair theorems are mathematical theorems that state that a black hole can be described by only a few parameters (mass, charge, and angular momentum) and that all other information is lost in the singularity. This means that all black holes of the same mass, charge, and angular momentum are identical, regardless of how they were formed.

4. Why is the concept of no-hair theorems important?

No-hair theorems are important because they help us understand the fundamental nature of black holes and their role in the universe. They also have implications for our understanding of gravity and the laws of physics in extreme conditions.

5. Are no-hair theorems universally accepted by scientists?

No-hair theorems are widely accepted by scientists, but there is ongoing research and debate about the validity of these theorems and their implications for our understanding of black holes. Some scientists argue that there may be ways to extract information from black holes, while others believe that the no-hair theorems hold true. Further research and observations are needed to fully understand the nature of black holes and their role in the universe.

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