The second law requires a generally-covariant extension. The statement is, roughly: in appropriate units, the sum of normal entropy and the area of black hole

The second law requires a generally-covariant extension. The statement is, roughly: in appropriate units, the sum of normal entropy and the area of black hole horizons is non-decreasing. See, for example, https://inspirehep.net/record/91796 https://inspirehep.net/record/91796 and literature surrounding "Generalized Second Law".