2021/02/28 by Kouji Nakamura · 8 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Deriving the Schwarzschild solution #Kerr metric #Magnetic monopole #Pulsars and Gravitational Waves Research #Quantum field theory in curved spacetime #Relativity and Gravitational Theory #Schwarzschild geodesics #Schwarzschild metric #Schwarzschild radius #Spacetime #Spherically symmetric spacetime #astro-ph.CO #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/ac03f9
published in Classical and Quantum Gravity 38(14), 145010 (IOP Publishing) · (v1) 10 pages, no figure; (v2) 16 pages, Section 2 is added for the explanation of our previous works, Additional explanations are added, references are added and re-organized; (v3) Some explanations are added, Typos are corrected
openalex created_date 2021/02/15 · arxiv created 2021/05/14 · openalex publication_date 2021/05/21 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
Abstract A gauge-invariant treatment of the monopole ( l = 0) and dipole ( l = 1) modes in linear perturbations of the Schwarzschild background spacetime is proposed. Through this gauge-invariant treatment, we derived the solutions to the linearized Einstein equation for these modes with a generic matter field. In the vacuum case, these solutions include the Kerr parameter perturbations in the l = 1 odd modes and the additional mass parameter perturbations of the Schwarzschild mass in the l = 0 even modes. The linearized version of Birkhoff’s theorem is also confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.