On the internal geometry of black hole perturbations

BERNARDO ARANEDA

Sao Paulo

Workshop; The Sound of Space-time: The Dawn of Gravitational Wave Science; 2018

ICTP-SAIFR

One of the major open problems in mathematical Relativity is the stability of black holes as solutions to the Einstein equations. After a brief review of the different approaches to the problem in its linear regime (Teukolsky, Regge-Wheeler and Zerilli equations, hidden symmetries, etc.), we show that there is an underlying symmetry structure from which all equations can be derived, and that it has its origin in the conformal and complex geometry of the space-time. In particular, this uncovers the geometrical meaning of the Teukolsky connection and of the hidden symmetries associated to Killing spinors and conformal Killing-Yano tensors.