# Most general definition of a black hole?

The standard definition of a black hole, which includes all the classic "stellar" black holes, is the complement of the past of future null infinity

$$\mathcal M \setminus I^-(\mathscr I^+)$$

That is, the set of points that cannot reach infinity.

This definition is fairly narrow, though. Is there a definition that would include such black holes as the Schwarzschild-de Sitter black hole (not asymptotically flat), or the elliptic Schwarzschild solution (not causal or time orientable)?

• In practical terms, we're using a black hole metric to approximate some quite small region of space, within a galaxy, so it really doesn't matter if there are other things happening at the cosmological scale. There has been some work on quasilocal definitions. See, e.g., Booth, arxiv.org/abs/gr-qc/0508107 . – user4552 Jun 29 '17 at 17:16
• Probably relevant: physics.stackexchange.com/questions/62175 – Kyle Kanos Jun 29 '17 at 17:24