On Black Hole Echoes

TL;DR

This paper models gravitational wave echoes from black hole mergers considering Lorentz symmetry violations, finding that such echoes are weak unless there are significant deviations from general relativity or effective field theory.

Contribution

It introduces a simple model for black hole echoes based on modified graviton dispersion relations, highlighting the conditions under which echoes could be detectable.

Findings

Weak echoes arise from Lorentz-violating dispersion relations.

Strong echoes require significant departures from standard GR.

Black hole horizons become weakly reflective in the model.

Abstract

We consider a very simple model for gravitational wave echoes from black hole merger ringdowns which may arise from local Lorentz symmetry violations that modify graviton dispersion relations. If the corrections are sufficiently soft so they do not remove the horizon, the reflection of the infalling waves which trigger the echoes is very weak. As an example, we look at the dispersion relation of a test scalar field corrected by roton-like operators depending only on spatial momenta, in Gullstrand-Painlev\'e coordinates. The near-horizon regions of a black hole do become reflective, but only very weakly. The resulting ``bounces" of infalling waves can yield repetitive gravity wave emissions but their power is very small. This implies that to see any echoes from black holes we really need an egregious departure from either standard GR or effective field theory, or both. One possibility to realize such strong echoes is the recently proposed classical firewalls which replace black hole horizons with material shells surrounding timelike singularities.