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Andrzej Rostworowski: A new perspective on metric gravitational perturbations of spherically symmetric spacetimes

Time: Thu 2019-12-05 11.00 - 12.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan

Participating: Andrzej Rostworowski, Jagiellonian University

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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).