Metric of a Multipartite AdS-Schwarzschild Black Hole In section 1 of Susskind's article (see https://arxiv.org/abs/1604.02589) on ER-EPR duality and its connection to the Everett and Copenhagen interpretation of quantum mechanics, he briefly studied multipartite AdS-Schwarzschild black holes (see figure 11). This drove me to wonder what metric would define such a spacetime?
 A: As far as I know all the explicit examples of multiboundary black holes and wormholes belong to $(2+1)$ gravity with negative cosmological constant. The metric for such solutions is locally anti-de Sitter spacetime.
Note, that in three dimensions the Einstein field equations fully determine the Riemann tensor, so there is no propagating graviton. To add curvature to a spacetime one could introduce cosmological constant. Positive $\Lambda$ imposes too rigid restrictions for the existence of even a single black hole solution, but for negative $\Lambda$ there is a well known BTZ black hole, so the multiboundary solutions are the generalizations of it.
Locally all such solutions are isometric to AdS3  spacetimes and are constructed by gluing together pieces of AdS3 or  alternatively by orbifolding universal covering space of AdS3 by some discrete group. 
Several examples for a multiboundary black holes are given in:


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*Brill, D. R. (1996). Multi-black-hole geometries in $(2+1)$–dimensional gravity. Physical Review D, 53(8), R4133, doi, arXiv:gr-qc/9511022.


Here is a figure from the paper describing construction of the three-black-hole solution:

Pictured here is a 2D hyperbolic manifold that serves as initial data for a full 3D spacetime (a $t=0$ slice). This manifold is constructed from two copies of Poincaré disk, with three lobes chopped off along ultraparallel geodesics and then glued together along the cuts. The full spacetime is built by evolving this initial data in time, when each of the three exterior regions would become the exterior of a BTZ black hole (without rotation), while interior is a sort of closed black hole cosmological spacetime.
