PreprintArticleVersion 1This version is not peer-reviewed
Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime
Version 1
: Received: 29 September 2024 / Approved: 30 September 2024 / Online: 30 September 2024 (15:26:24 CEST)
How to cite:
Nakamura, K. Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime. Preprints2024, 2024092444. https://doi.org/10.20944/preprints202409.2444.v1
Nakamura, K. Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime. Preprints 2024, 2024092444. https://doi.org/10.20944/preprints202409.2444.v1
Nakamura, K. Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime. Preprints2024, 2024092444. https://doi.org/10.20944/preprints202409.2444.v1
APA Style
Nakamura, K. (2024). Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime. Preprints. https://doi.org/10.20944/preprints202409.2444.v1
Chicago/Turabian Style
Nakamura, K. 2024 "Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l = 0, 1 Mode Perturbations on the Schwarzschild Background Spacetime" Preprints. https://doi.org/10.20944/preprints202409.2444.v1
Abstract
Comparison of the gauge-invariant formulation for l=0,1-mode perturbations on the Schwarzschild background spacetime proposed in [K. Nakamura, Class. Quantum Grav. 38 (2021), 145010.] and a “conventional complete gauge-fixing approach” in which we use the spherical harmonic functions Ylm as the scalar harmonics from the starting point is discussed. Although it is often said that “gauge-invariant formulations in general-relativistic perturbations are equivalent to complete gauge-fixing approaches,” as the result of this comparison, we conclude that the derived solutions through the proposed gauge-invariant formulation and those through a “conventional complete gauge-fixing approach” are different. It is pointed out that there is a case where the boundary conditions and initial conditions are restricted in a conventional complete gauge-fixing approach.
Keywords
black hole; Schwarzschild spacetime; perturbation theory; gauge-invariance; gauge-fixing
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.
