AdS perspective on the nonlinear tails in black hole ringdowns

Black holes gradually settle into their static configuration by emitting gravitational waves, whose amplitudes 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>AdS</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> <a:mo>×</a:mo> <a:mrow> <a:msup> <a:mrow> <a:mi mathvariant="normal">S</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:mrow> </a:mrow> </a:math> spacetime perspective with their amplitudes being related to the Aretakis constants.