Non-Linear Black Hole Ringdown

Abstract

Imprints of non-linear effects of gravity are present in the quasi-normal modes of a black hole during its ringdown phase. In this work, we use methods to analytically calculate these non-linearities in the near horizon and near infinity regime. First, we approximate the Zerilli potential with the Pöschl-Teller potential and see the problems that arise using this method and how to tackle them. Second, we get the approximate solutions to the Zerilli equations using the WKB approximation and use them to evaluate the components needed to calculate the non-linearities. We then calculate these non-linearities at infinity and horizon. We also see that our values are close to values attained by recent numerical results.