Gravitational and electromagnetic perturbations of a charged black hole in a general gauge condition

Abstract

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordström geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function ${\Psi }_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $\chi$ which relates the perturbations of the radiative Maxwell scalars ${\phi }_2$ and the Weyl scalar ${\Psi }_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhar's book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordström spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal.

21 pages, 6 figures, 1 table

References in corpus (2)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• LIGO: The Laser Interferometer Gravitational-Wave Observatory

Cited by in corpus (1)

• Self-interacting scalar field distributions around Schwarzschild black holes