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

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Discussion Overview

The discussion revolves around the definition of "black hole" in the context of no-hair theorems, particularly as presented in a review article. Participants explore the implications of different definitions and the conditions under which the no-hair theorem applies, including considerations of event horizons and asymptotic flatness.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how "black hole" is defined in the context of no-hair theorems, noting a lack of explicit definition in the review article.
  • Concerns are raised about whether a black hole can be defined as any electrovac solution with a singularity, suggesting this would imply a proof of cosmic censorship, which remains unproven.
  • Another participant suggests that the definition may be effectively illustrated in a figure from the article, indicating that a black hole is characterized by having an event horizon.
  • It is noted that asymptotic flatness is important for defining what "escape to infinity" means, with the black hole region being defined as the area from which escape to future null infinity is impossible.
  • A reference is made to another article that explores different characterizations of black holes, although it is unclear if it addresses the concept of "hair."

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definition of black holes in the context of no-hair theorems, with no consensus reached on the implications of various definitions or the assumptions involved.

Contextual Notes

Participants highlight potential limitations in the definitions provided, including assumptions about asymptotic flatness and the nature of singularities, without resolving these issues.

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 \Lambda=0 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.
 


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.
 


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".
 

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