Is there a geometric reason why two merging black holes never “decay” into two separate black holes

This geometric reason for that statement is that there is only one null geodesic lying on the horizon going through each point of the horizon. If the black hole have split into two, then there would be a point on the horizon from which two different null geodesics lying within the horizon would start, which is impossible. So black holes could form (starting with one point from which all of the horizon springs into existance) and merge, but not bifurcate.

This is not a consequence of the Hawking area theorem but was also formulated by Hawking:

• Hawking, S. W. (1972). Black holes in general relativity. Communications in Mathematical Physics, 25(2), 152-166, doi, OA text at ProjectEuclid. (section 2, p. 156).

See also the Book:

• Hawking, S. W., & Ellis, G. F. R. (1973). The large scale structure of space-time. Cambridge University Press, Chapter 9.

As $\tau$ increases, black holes can merge together, and new black holes can form as the result of further bodies collapsing. However, the following result shows that black holes can never bifurcate.

The following result is a proposition 9.2.5 which simply formally states that.

Incidentally, it seems that this property has no generalization in higher dimensions where for example black strings (extended black holes with horizon topology of, say, $R_2\times S_2$ for 5D gravity) would fragment into many snaller black holes as a result of Gregory–Laflamme instability.

• Lehner, L., & Pretorius, F. (2011). Final state of Gregory-Laflamme instability. arXiv:1106.5184.