The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown

TL;DR

This paper explores the nonlinear tail behavior in black hole ringdown by using the AdS$_2$$\times$S$^2$ spacetime framework, revealing their connection to Aretakis constants and potential dominance over linear tails.

Contribution

It introduces a novel approach to derive nonlinear tails in black hole physics from the AdS$_2$$\times$S$^2$ perspective, linking them to Aretakis constants.

Findings

Nonlinear tails can be derived from the AdS$_2$$\times$S$^2$ perspective.

Nonlinear tails may dominate over linear tails in black hole ringdown.

Amplitudes of tails relate to Aretakis constants.

Abstract

Black holes gradually settle into their static configuration by emitting gravitational waves, whose amplitude diminish over time according to a power-law decay at fixed spatial locations. We show that the nonlinear tails in the presence of a quadratic source, which have been recently found to potentially dominate over the linear ones, can be simply derived from the AdS$_2$$\times$S$^2$ spacetime perspective with their amplitudes being related to the Aretakis constants.