Version 1
: Received: 25 October 2024 / Approved: 25 October 2024 / Online: 25 October 2024 (13:00:34 CEST)
How to cite:
Nakamura, K. Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part II: — Even-Mode Perturbations —. Preprints2024, 2024102048. https://doi.org/10.20944/preprints202410.2048.v1
Nakamura, K. Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part II: — Even-Mode Perturbations —. Preprints 2024, 2024102048. https://doi.org/10.20944/preprints202410.2048.v1
Nakamura, K. Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part II: — Even-Mode Perturbations —. Preprints2024, 2024102048. https://doi.org/10.20944/preprints202410.2048.v1
APA Style
Nakamura, K. (2024). Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part II: — Even-Mode Perturbations —. Preprints. https://doi.org/10.20944/preprints202410.2048.v1
Chicago/Turabian Style
Nakamura, K. 2024 "Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part II: — Even-Mode Perturbations —" Preprints. https://doi.org/10.20944/preprints202410.2048.v1
Abstract
This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the gauge-invariant treatments for l=0,1 mode perturbations on the Schwarzschild background spacetime in the Part I paper [K. Nakamura, arXiv:2110.13508 [gr-qc]], we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including l=0,1 modes. Furthermore, we explicitly derive the l=0,1 mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for l=0 mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the l=0,1-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper.
Keywords
black hole; Schwarzschild spacetime; perturbation theory; gauge-invariance
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
