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arXiv · 2307.01587

ICRC2023 Proceedings: Proposal of a gauge-invariant treatment of $l=0,1$-mode perturbations on the Schwarzschild background spacetime

Kouji Nakamura
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Abstract

A gauge-invariant perturbation theory on a generic background spacetime is developing from 2003 and ``zero-mode problem'' for linear metric perturbations was proposed as the essential problem of this theory. In the perturbation theory on the Schwarzschild background spacetime, $l=0,1$ modes correspond to the above ``zero-mode'' and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. Due to this situation, a gauge-invariant treatment for these $l=0,1$-mode perturbations is proposed. Through this gauge-invariant treatment, the solutions to the linearized Einstein equation for these modes with a generic matter field are derived. In the vacuum case, the linearized version of uniqueness theorem of Kerr spacetime is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.

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Kouji Nakamura. 2023-07-04. ICRC2023 Proceedings: Proposal of a gauge-invariant treatment of $l=0,1$-mode perturbations on the Schwarzschild background spacetime. https://arxiv.org/abs/2307.01587

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