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)?
