Black holes in a box: towards the numerical evolution of black holes in AdS

TL;DR

This paper investigates the evolution of black hole binaries in a confined AdS-like setting with reflective boundary conditions, analyzing post-merger dynamics and radiation absorption over multiple reflections.

Contribution

It demonstrates the numerical evolution of black hole binaries in a box with mirror-like boundaries, highlighting the effects of boundary conditions on radiation and angular momentum transfer.

Findings

Approximately 15% of radiation energy is absorbed per boundary reflection.

Angular momentum transfer occurs only during the first interaction.

Numerical data confirms relations between Newman-Penrose scalars _4 and _0.

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 non-globally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data is supplemented by boundary conditions at the time-like 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 mirror-like 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 only observed in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both the Newman-Penrose scalars \Psi_4 and \Psi_0 are non-trivial in our setup, and we show that the numerical data verifies the expected relations between them.