Following Hawking and Ellis, Chapter 9, Fig. 60, Pg. 322, the following figure is meant to illustrate the contrast between apparent horizons and event horizons in the case of a binary black hole merger.
I understand the merger of two black holes in the long run settles into a Kerr black hole, and I more or less understand why this is correct. But, I wonder if there exists any simple solution of the binary black hole merger that can actually illustrate this phenomenon? Does there exist any simple metric solution to the Einstein's Field equation that models the black hole merger to illustrate the above concept in explicit form?