On the charge of the Galactic centre black hole

TL;DR

This paper investigates the possible electric charge of the Galactic centre black hole, providing realistic limits, discussing charging mechanisms, and proposing an observational test to constrain its charge more tightly.

Contribution

It offers new estimates of the SMBH charge, analyzes charging and discharging timescales, and introduces a novel observational method to detect small charges.

Findings

Classical charge limit is $ extless 10^9$ C, transient on viscous timescale.

Induced charge from magnetic fields can be up to $ extless 10^{15}$ C, likely positive.

Current observational limit on Sgr A*'s charge is $ extless 3 imes 10^{8}$ C.

Abstract

The Galactic centre supermassive black hole (SMBH), in sharp contrast with its complex environment, is characterized by only three classical parameters -- mass, spin, and electric charge. Its charge is poorly constrained. It is, however, usually assumed to be zero because of neutralization due to the presence of plasma. We revisit the question of the SMBH charge and put realistic limits on its value, timescales of charging and discharging, and observable consequences of the potential, small charge associated with the Galactic centre black hole. The electric charge due to classical arguments based on the mass difference between protons and electrons is $\lesssim 10^9\,{\rm C}$ and is of a transient nature on the viscous time-scale. However, the rotation of a black hole in magnetic field generates electric field due to the twisting of magnetic field lines. This electric field can be associated with induced charge, for which we estimate an upper limit of $\lesssim 10^{15}\,{\rm C}$. Moreover, this charge is most likely positive due to an expected alignment between the magnetic field and the black-hole spin. Even a small charge of this order significantly shifts the position of the innermost stable circular orbit (ISCO) of charged particles. In addition, we propose a novel observational test based on the presence of the bremsstrahlung surface brightness decrease, which is more sensitive for smaller unshielded electric charges than the black-hole shadow size. Based on this test, the current upper observational limit on the charge of Sgr A* is $\lesssim 3\times 10^{8}\,{\rm C}$.