Are There Exact Black Hole Solutions in Non-Asymptotically Flat Spacetimes?

[old dog]

Are there any EXACT solutions similar to Schwarzschild or Kerr in a spacetime which is not asymptotically flat; e.g. FLRW or other cosmological metrics? I am already familiar with the "Swiss cheese" approximations.

 

[jedishrfu]

If you believe wikipedia then there are only 4 known solutions:

http://en.wikipedia.org/wiki/Rotating_black_hole

and

http://en.wikipedia.org/wiki/Einstein's_equations

 

[Ben Niehoff]

We also have exact solutions for the 4 basic black holes in asymptotically de Sitter or anti de Sitter spacetimes. De Sitter spacetime corresponds to eternal inflation.

 

[George Jones]

Isn't "Swiss Cheese" exactly what you want? A single hole version of this is the classic paper "Conformal Structure of a Schwarzschild Black Hole Immersed in a Friedman Universe" by Sussman ("General Relativity and Gravitation, Vol. 17, No. 3, 1985) Abstract:

The evolution of a Schwarzschild black hole in an expanding Friedman universe is described using the same coordinate patch for both geometries. Comoving and extended Kruskal coordinates are considered and compared for the cases k = 0 and k = 1. The conformal structure and some global topological aspects of the Schwarzschild-Friedman system are examined with the help of diagrams in comoving and extended Kruskal coordinates.

 

[sardar]

I can say that there are currently no exact solutions for black holes in a non-asymptotically flat spacetime. While there have been attempts to find solutions similar to Schwarzschild or Kerr in a FLRW or other cosmological metrics, these have only resulted in "Swiss cheese" approximations which are not exact solutions.

The difficulty in finding exact solutions lies in the complex nature of the equations governing black holes in non-asymptotically flat spacetimes. These equations involve not only the properties of the black hole, but also the curvature and expansion of the surrounding spacetime. This makes it challenging to find a single exact solution that can accurately describe a black hole in a non-asymptotically flat spacetime.

However, scientists are constantly working to refine and improve our understanding of black holes in various spacetimes. With advancements in technology and theoretical models, it is possible that in the future we may be able to find more accurate and exact solutions for black holes in non-asymptotically flat spacetimes. But for now, the "Swiss cheese" approximations remain the best approximation we have.