Towards the construction of multi-centered black holes in AdS

We find a class of approximate perturbative solutions describing multi-centered BPS black holes in asymptotically AdS$_4$. These black holes are moving coplanarly in a circular orbit with common radius but fixed phase differences, where the radius is characterized by a common boost velocity $v$. While the solutions are not complete, as they are only accurate up to $\mathcal{O}(M^2v^2)$, we are able to locally investigate their supersymmetric properties in four-dimensional $\mathcal{N} = 2$ supergravity. The result indicates that, while a single BPS black hole preserves half of the supersymmetries, a configuration with two or more black holes is only 1/4 BPS. These perturbative solutions reduce in the asymptotically Minkowski limit to the multi-black hole solution of Majumdar and Papapetrou.