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 ($l=0$) and dipole ($l=1$) 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.

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)

Cited by in corpus (4)

• Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part III: -- Realization of exact solutions