[Paper Review] Electric charge of black holes: Is it really always negligible?

Michal Zajaček, Arman Tursunov|arXiv (Cornell University)|Apr 9, 2019

Astrophysical Phenomena and ObservationsPhysics and Astronomy28 citations

TL;DR

This paper challenges the widespread assumption that black hole electric charge is negligible in astrophysical models. It demonstrates that even small charges—on the order of 10⁸ C for the Galactic center black hole—can produce electromagnetic forces on charged particles (e.g., cosmic rays) that are up to 16 times stronger than gravity, significantly altering particle dynamics and ISCO positions, thus making charge a non-negligible factor in high-energy astrophysics and multi-messenger astronomy.

ABSTRACT

We discuss the problem of the third black hole parameter, an electric charge. While the mass and the spin of black holes are frequently considered in the majority of publications, the charge is often neglected and implicitly set identically to zero. However, both classical and relativistic processes can lead to a small non-zero charge of black holes. When dealing with neutral particles and photons, zero charge is a good approximation. On the other hand, even a small charge can significantly influence the motion of charged particles, in particular cosmic rays, in the vicinity of black holes. Therefore, we stress that more attention should be paid to the problem of a black-hole charge and hence, it should not be neglected a priori, as it is done in most astrophysical studies nowadays. The paper looks at the problem of the black-hole charge mainly from the astrophysical point of view, which is complemented by a few historical as well as philosophical notes when relevant. In particular, we show that a cosmic ray or in general elementary charged particles passing a non-neutral black hole can experience an electromagnetic force as much as sixteen times the gravitational force for the mass of the Galactic centre black hole and its charge being seventeen orders of magnitude less than the extremal value (calculated for a proton). Furthermore, a Kerr-Newman rotating black hole with the maximum likely charge of 1 Coulomb per solar mass can have the position of its innermost stable circular orbit (ISCO) moved by both rotation and charge in ways that can enhance or partly cancel each other, putting the ISCO not far from the gravitational radius or out at more than 6 gravitational radii. An interpretation of X-ray radiation from near the ISCO of a black hole in X-ray binaries is then no longer unique.

Motivation & Objective

• To challenge the common astrophysical assumption that black hole electric charge is negligible and can be set to zero.
• To investigate the physical mechanisms by which black holes could acquire non-zero charge, including thermal equilibrium and Wald's induction mechanism.
• To assess the observable consequences of non-zero black hole charge on the motion of charged particles, particularly cosmic rays.
• To examine how black hole charge influences the location of the innermost stable circular orbit (ISCO), complicating the interpretation of X-ray emissions.
• To argue that charge should be considered a non-trivial parameter in modeling black hole accretion and energy extraction processes.

Proposed method

• Analyzes the equilibrium charge-to-mass ratio of macroscopic bodies using the Maxwell-Boltzmann distribution in conservative gravitational and electric fields, deriving Qeq/M• ≈ 76.9 C/M⊙.
• Applies Wald's 1974 mechanism to model charge induction in rotating black holes immersed in external magnetic fields, with Q• = 2a•M•Bext.
• Uses the Kerr-Newman metric to model the spacetime of charged, rotating black holes and computes the ISCO for charged test particles.
• Compares the ratio of electrostatic to gravitational forces on protons and electrons near a black hole, showing Felstat/Fgrav ≈ 16 for Q• ≈ 10⁸ C and M• ≈ 4×10⁶ M⊙.
• Constructs ISCO location maps (Figure 1) as a function of black hole charge for electrons and protons, showing shifts up to 9 gravitational radii.
• Evaluates the degeneracy between spin, charge, and magnetic fields in shifting the ISCO, leading to non-unique interpretations of X-ray light curves.

Experimental results

Research questions

• RQ1 Can black holes acquire a non-zero electric charge through thermodynamic or relativistic mechanisms?
• RQ2 How strong is the electromagnetic force on a charged particle (e.g., proton) near a black hole compared to gravity, given a small but non-zero charge?
• RQ3 To what extent can electric charge mimic or alter the effects of black hole spin on the location of the ISCO?
• RQ4 Can the observed ISCO in X-ray binaries or the Galactic center be uniquely attributed to spin, or could charge or magnetic fields be responsible?
• RQ5 What are the implications of non-zero black hole charge for the origin of ultra-high-energy cosmic rays?

Key findings

• The electrostatic force on a proton near a 4×10⁶ M⊙ black hole with a charge of 10⁸ C exceeds the gravitational force by a factor of 16.
• A black hole with a charge of 3.3×10⁵ C can shift the ISCO for electrons to 9 gravitational radii, mimicking a retrograde spin.
• For protons, a negative charge of 6.0×10⁸ C or a positive charge of 5.07×10⁹ C can similarly push the ISCO to 9rg.
• The presence of a circumnuclear magnetic field can also shift the ISCO, creating a degeneracy with charge and spin in ISCO interpretation.
• The innermost stable circular orbit (ISCO) for a non-rotating black hole can be displaced from 6rg to 9rg due to electric charge alone, even for small charges.
• The Blandford-Znajek mechanism, which extracts rotational energy via electromagnetic fields, is driven by the black hole's charge, implying charge is essential for jet formation.