On the charge of the Galactic centre black hole

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 10 9 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 10 15 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 3 × 10 8 C.

Fifty Years of Energy Extraction from Rotating Black Hole: Revisiting Magnetic Penrose Process

“…Thus, the assumption of the Kerr hypothesis is well founded. However, it would turn out, as we show below, that black hole charge would play crucial role in making energy extraction process ultra-efficient, so much so that efficiency could range over 10 10 . In the next section, we describe the black hole charging mechanisms in astrophysical context and discuss its possible screening by surrounding plasma.…”

“…Maximal theoretical value of the charge of a black hole of mass M is given by Q = 2G 1/2 M, written in Gaussian units. For spinning black hole, it is of order [10]…”

Constraining the charge of the Galactic centre black hole

“…On the other hand, the characterstic ordered charge oscillations of the plasma (plasma frequency) and cyclotron motions take place on much shorter timescales than the viscous or free-fall timescale. For details, see the analysis presented in [43].…”

Seeing relativity-II: Revisiting and visualizing the Reissner–Nordström metric

“…(15), one to an orthonormal vector spanned by ∂/∂r, i.e., the vector defined in Eq. (20), R µ stat , and two normal vectors spanned by ∂/∂ϕ and ∂/∂θ, Φ µ and Θ µ . By suitably choosing an orientation of the coordinate system, a null geodesic is of the form…”