Question on Black Hole Metrics

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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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