The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown

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.