Formal solutions of any-order mass, angular-momentum, dipole perturbations on the Schwarzschild background spacetime
Abstract
Formal solutions of any-order mass, angular-momentum, dipole perturbations on the Schwarzschild background spacetime are derived in a gauge-invariant manner. Once we accept the proposal in [K. Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.], we can extend the gauge-invariant linear perturbation theory on the Schwarzschild background spacetime including the monopole () and dipole () modes to any-order perturbations of the same background spacetime through the arguments in [K. Nakamura, Class. Quantum Grav. {\bf 31} (2014), 135013.]. As a result of this resolution, we reached to a simple derivation of the above formal solutions of any order.
Keywords
Cite
@article{arxiv.2102.10650,
title = {Formal solutions of any-order mass, angular-momentum, dipole perturbations on the Schwarzschild background spacetime},
author = {Kouji Nakamura},
journal= {arXiv preprint arXiv:2102.10650},
year = {2021}
}
Comments
10 pages, no figure. arXiv admin note: text overlap with arXiv:2102.00830 (v1), arXiv:1403.1004; 11 pages no figure. The whole presentations are changed and references are re-organized and added, although the main assertion of this paper is unchanged. (v2); introduction is changed, references are added. (v3)