Question on Black Hole Metrics

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SUMMARY

The discussion centers on the existence of black holes in non-asymptotically flat (non-AF) spacetimes. It establishes that traditional definitions of black holes, which rely on the concept of null infinity, do not apply in non-AF spacetimes. However, solutions like the Schwarzschild deSitter metric are acknowledged as representations of black holes in such universes. The conversation also touches on the implications of light behavior in these contexts, questioning the nature of escape from a black hole when infinity is not defined.

PREREQUISITES
  • Understanding of general relativity concepts
  • Familiarity with asymptotically flat spacetimes
  • Knowledge of the Schwarzschild deSitter metric
  • Basic grasp of event horizons and null infinity
NEXT STEPS
  • Research the implications of non-asymptotically flat spacetimes in general relativity
  • Study the Schwarzschild deSitter solution in detail
  • Explore the concept of event horizons in various spacetime geometries
  • Investigate the behavior of light in curved spacetime
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The discussion is beneficial for theoretical physicists, cosmologists, and students of general relativity who are exploring advanced concepts related to black holes and spacetime geometries.

skippy1729
Are there any exact solutions known for a black hole in a universe which is NOT asymptotically flat?
 
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Yes and no. Technically, the notion of a black hole doesn't make sense in a non AF spacetime. An event horizon is defined as the boundary of the past of future null infinity, but there's no such thing as null infinity if the spacetime is not AF. (Intuitively, a black hole is a region of spacetime from which nothing can escape--but if there's no infinity, what does "escape" even mean?)

However, there are some solutions, like Schwarzschild deSitter, which most people would say represent "a black hole in a non-AF universe".
 
Sam Gralla said:
An event horizon is defined as the boundary of the past of future null infinity, but there's no such thing as null infinity if the spacetime is not AF. (Intuitively, a black hole is a region of spacetime from which nothing can escape--but if there's no infinity, what does "escape" even mean?)
So you think radially rising light has some kind of apogee?
 

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