Slowly rotating black holes in the novel Einstein–Maxwell-scalar theory

Jianhui Qiu

doi:10.1140/epjc/s10052-021-09890-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 1094
https://doi.org/10.1140/epjc/s10052-021-09890-3

Regular Article - Theoretical Physics

Slowly rotating black holes in the novel Einstein–Maxwell-scalar theory

Jianhui Qiu¹^,2^a

¹ National Astronomical Observatories, Chinese Academy of Sciences, 100101, Beijing, China
² School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, No. 19A, Yuquan Road, 100049, Beijing, China

^a jhqiu@nao.cas.cn

Received: 12 October 2021
Accepted: 28 November 2021
Published online: 12 December 2021

Abstract

We investigate a slowly rotating black hole solution in a novel Einstein–Maxwell-scalar theory, which is prompted by the classification of general Einstein–Maxwell-scalar theory. The gyromagnetic ratio of this black hole is calculated, and it increases as the second free parameter $β$ $\beta$ increases, but decreases with the increasing parameter $γ \equiv \frac{2 α^{2}}{1 + α^{2}}$ $\gamma \equiv \frac{2 \alpha ^{2}}{1+\alpha ^2}$ . In the Einstein–Maxwell-dilaton (EMD) theory, the parameter $β$ $\beta$ vanishes but the free parameter $α$ $\alpha$ governing the strength of the coupling between the dilaton and the Maxwell field remains. The gyromagnetic ratio is always less than 2, the well-known value for a Kerr–Newman (KN) black hole as well as for a Dirac electron. Scalar hairs reduce the magnetic dipole moment in dilaton theory, resulting in a drop in the gyromagnetic ratio. However, we find that the gyromagnetic ratio of two can be realized in this Einstein–Maxwell-scalar theory by increasing $β$ $\beta$ and the charge-to-mass ratio Q/M simultaneously (recall that the gyromagnetic ratio of KN black holes is independent of Q/M). The same situation also applies to the angular velocity of a locally non-rotating observer. Moreover, we analyze the period correction for circular orbits in terms of charge-to-mass ratio, as well as the correction of the radius of the innermost stable circular orbits. It is found the correction increases with $β$ $\beta$ but decreases with Q/M. Finally, the total radiative efficiency is investigated, and it can vanish once the effect of rotation is considered.

© The Author(s) 2021

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