Non-linear Quasi-Normal Modes of the Schwarzschild Black Hole from the Penrose Limit
Abstract
The Penrose limit connects a plane wave geometry to the photon ring of a black hole, where the quasi-normal modes are located in the eikonal limit. Utilizing this simplification, we analytically extract the quadratic-level non-linearities in the quasi-normal modes of a Schwarzschild black hole for the (×) 2 channel. We demonstrate that this result is independent of and further confirm it through symmetry arguments.
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