A new perspective on metric gravitational perturbations of spherically symmetric spacetimes

General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

05 December 11:00 - 12:00

Andrzej Rostworowski - Jagiellonian University

The key result of Schwarzschild black hole metric perturbation theory is that at the linear level a general perturbation can be given in terms of only two (axial/polar) master scalars satisfying scalar wave equation on the Schwarzschild background with Regge-Wheeler and Zerilli potentials for axial and polar sectors respectively (more precisely, this holds for any multipole $\ell \geq 2$; the monopole $\ell=0$ and dipole $\ell=1$ cases need some special treatment). While this remarkable result is usually obtained by tedious manipulations with linearized Einstein equations, I will show that it can be conceptually easily obtained starting with the \textit{ansatz} that all gauge invariant characteritics of perurbations (for a given $\ell>1$ multipole) are given in terms of a master scalar and its derivatives, where the master scalar satisfies a scalar wave equation (with a potential) on the background solution. This new perspective can be easily extended beyond linear approximation where it was used to provide the evidence for the existence of globally regular, asymptotically-AdS, time-periodic solutions of Einstein equations. It can be also easily generalised to include matter, either in the form of some fundamental fields (studied for example in the AdS/CFT context) or effective perfect fluid approximation (for example in the context of cosmological perturbations). The talk will be mainly based on the paper Phys. Rev. D96, 124026 (2017).
Lars Andersson
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Mattias Dahl
KTH Royal Institute of Technology
Philippe G. LeFloch
Sorbonne University
Richard Schoen
University of California, Irvine


Mattias Dahl


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