Reflecting boundary conditions in numerical relativity as a model for black hole echoes

Abstract

Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before reaching the horizon. There does not seem to be a good understanding of how to properly model a reflecting surface in numerical relativity, as the vast majority of the literature avoids the implementation of artificial boundaries, or applies transmitting boundary conditions. Here, we present a framework for reflecting a scalar field in a fully dynamical spherically symmetric spacetime, and implement it numerically. We study the evolution of a wave packet in this situation and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole. This opens the door to model exotic near-horizon physics within full numerical relativity.

12 pages, 6 figures, updated to final published version

References in corpus (6)

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• Solving Einstein's Equations With Dual Coordinate Frames
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
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Cited by in corpus (4)

• Nonlinear treatment of a black hole mimicker ringdown
• Boson star superradiance with spinning effects and in time domain
• Black hole spectroscopy and nonlinear echoes in Einstein-Maxwell-scalar theory
• Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes