Abstract
Testing black hole’s charged property is a fascinating topic in modified gravity and black hole astrophysics. In the first Gravitational-Wave Transient Catalog (GWTC-1), ten binary black hole merger events have been formally reported, and these gravitational wave signals have significantly enhanced our understanding of the black hole. In this paper, we try to constrain the amount of electric charge with the parameterized post-Einsteinian framework by treating the electric charge as a small perturbation in a Bayesian way. We find that the current limits in our work are consistent with the result of Fisher information matrix method in previous works. We also develop a waveform model considering a leading order charge effect for binary black hole inspiral.
Highlights
Case, the discharge process is much slower than for ordinary plasma so the charged black hole (BH) are viable
To characterize gravitational wave (GW), we often use inspiral, merger and ringdown to describe the whole coalescence of a binary BH, where the inspiral stage is generally described by post-Newtonian theory [18], merger stage is generally approximated by the numerical simulation [19], and ringdown stage is described by the BH perturbation theory [20,21]
For three reasons: first, the phase before tISCO can be included in φc and the effect is equal to a time shift, which means this does not affect the results of parameter estimation; second, ωgw is infinity when τ = 0, and this can not be integrated; last but not least, the leading order charged (LOC) waveform model cannot truly describe the motion of the binary BH when the orbital distance is too small
Summary
At present, using the shadow of supermassive BH to estimate its charge has been developed and widely practiced [11], for example Sgr A* and M87* measured by VLBI [12,13,14,15]. C (2021) 81:769 the parameterized post-Einsteinian (ppE) framework [16] In this case, the correction due to the electric dipole radiation is completely described by the coefficient of the −1 postNewtonian (PN) order in the waveform, the rest part of the waveform is the same as that of the accurate waveform model describing the coalescence of two neutral black holes, such as the well-known phenomenological waveform model [22]. 5. In this work, based on IMR waveform model in LIGOVirgo Algorithm Library [24], we use the Bayesian method to test the dipole radiation of GW signals [25,26] with the ppE framework.
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