Transfer of area from one black hole to another, without a merger? 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?
 A: This should really just be a comment, because I have not worked through the proof and can't offer any intuition, but the following excerpts from reputable sources seem to answer the question. The first source outlines the proof, and the second source (which cites the first) states the conclusion more clearly.

As time increases, black holes may merge together and new black holes may be created by further bodies collapsing but a black hole can never bifurcate. 



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*S. W. Hawking (1972), "Black holes in general relativity," Communications in Mathematical Physics 25: 152-166, https://projecteuclid.org/euclid.cmp/1103857884, specifically page 156



In thermodynamics one can transfer entropy from one system to another, and it is required only that the total entropy does not decrease. However one cannot transfer area from one black hole to another since black holes cannot bifurcate ([1, 2, 3]). Thus the second law of black hole mechanics requires that the area of each individual black hole should not decrease.



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*Bardeen, Carter, and Hawking (1973), "The Four Laws of Black Hole Mechanics," Communications in Mathematical Physics 31: 161-170, https://projecteuclid.org/euclid.cmp/1103858973, specifically page 168


Of course, these statements assume classical general relativity. The weak energy condition also seems to be assumed.
