Black holes in a box: Toward the numerical evolution of black holes in AdS space-times

Abstract

The evolution of black holes in "confining boxes" is interesting for a number of reasons, particularly because it mimics the global structure of anti–de Sitter geometries. These are nonglobally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data are supplemented by boundary conditions at the timelike conformal boundary. Here, we explore the active role that boundary conditions play in the evolution of a bulk black hole system, by imprisoning a black hole binary in a box with mirrorlike boundary conditions. We are able to follow the post-merger dynamics for up to two reflections off the boundary of the gravitational radiation produced in the merger. We estimate that about 15% of the radiation energy is absorbed by the black hole per interaction, whereas transfer of angular momentum from the radiation to the black hole is observed only in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both of the Newman-Penrose scalars Ψ4 and Ψ0 are nontrivial in our setup, and we show that the numerical data verifies the expected relations between them.

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