• Corpus ID: 239885316

Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations

@inproceedings{Nakamura2021GaugeinvariantPT,
  title={Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations},
  author={Kouji Nakamura},
  year={2021}
}

• Kouji Nakamura
• Published 26 October 2021
• Physics

This is the Part I paper of our series of papers on a gauge-invariant linear perturbation theory on the Schwarzschild background spacetime. We first review our general framework of the gauge-invariant perturbation theory, which can be easily extended to the higher-order perturbation theory. After that, we propose the strategy of the gauge-invariant linear perturbation theory on the Schwarzschild spacetime. In the above general framework, the “zero-mode problem” was a remaining important problem to develop higher-order gauge-invariant perturbation theories on generic background spacetime. In perturbation theories on the Schwarzschild background spacetime, l = 0 , 1-mode problem corresponds to the above “zero-mode problem.” The above strategy proposed in this paper is a resolution of this l = 0 , 1-mode problem in linear perturbations on the Schwarzschild background spacetime. Owing to this strategy, we can easily extend to higher-order perturbation theory. Following this proposal, we derive the linearized Einstein equations for any modes of l ≥ 0 in gauge-invariant manner. We discuss the solutions to the odd-mode perturbation equations in the linearized Einstein equations and show that these perturbations include the Kerr parameter perturbation in these odd-mode perturbation, which is physically reasonable. In the Part II and Part III papers [K. Nakamura, arXiv:2110.13512 [gr-qc]; arXiv:2110.13519 [gr-qc].] of this series of papers, we will show that the even-mode solutions to the linearized Einstein equations obtained through our proposal are also physically reasonable. Then, we conclude that our proposal of the resolution of the l = 0 , 1-mode problem is also physically reasonable.