Hawking and Ellis state the second law of black hole thermodynamics as their Proposition 9.2.7 (p. 318), in language that is a little opaque to me. Below the formal statement of the theorem, they give an interpretation, which talks about black holes growing and black holes merging in such a way that the total area increases.
In ordinary thermodynamics, there are processes in which one object's entropy goes down, but another object's entropy increases by a greater amount. Is this possible for black holes? In other words, is it possible for two black holes to interact without merging, in such a way that the total area increases? If so, then what would this interaction process look like? If not, then why not?