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

Conner Dailey, Niayesh Afshordi, Erik Schnetter

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.

Introduction

Both in the context of gravitational waves (GWs) and scalar waves, there has been a recent interest in black hole echoes. The idea behind black hole echoes is that there may be some mechanism, resulting from quantum phenomena for example, by which wave packets falling into a black hole could partially reflect off of an interface before reaching the horizon, thus resulting in a potentially detectable effect. In the context of GW astronomy, this has opened a novel window to study exotic near-horizon physics phenomenologically, from current and future observations. However, interpreting this data requires modelling strong gravitational systems in numerical relativity, where there does not currently seem to be a good understanding of how to properly implement a reflecting surface. There has also been some recent skepticism that black hole echoes can be detected at all due tothe formation of an apparent horizon before the reflection occurs, and having a proper way to model reflecting surfaces allows for rigorous testing beyond order-of-magnitude estimates.