Multi-centered black holes with a negative cosmological constant

Abstract

We present a recipe that allows to construct multi-centered black holes embedded in an arbitrary FLRW universe. These solutions are completely determined by a function satisfying the conformal Laplace equation on the spatial slices $\text{E}^3$, $\text{S}^3$ or $\text{H}^3$. Since anti-de Sitter space can be written in FLRW coordinates, this includes as a special case multi-centered black holes in AdS, in the sense that, far away from the black holes, the energy density and the pressure approach the values given by a negative cosmological constant. We study in some detail the physical properties of the single-centered asymptotically AdS case, which does not coincide with the usual Reissner-Nordström-AdS black hole, but is highly dynamical. In particular, we determine the curvature singularities and trapping horizons of this solution, compute the surface gravity of the trapping horizons, and show that the generalized first law of black hole dynamics proposed by Hayward holds in this case. It turns out that the spurious big bang/big crunch singularities that appear when one writes AdS in FLRW form, become real in presence of these dynamical black holes. This implies that actually only one point of the usual conformal boundary of AdS survives in the solutions that we construct. Finally, a generalization to arbitary dimension is also presented.