Schwarzschild black holes as unipolar inductors: expected electromagnetic power of a merger

TL;DR

This paper models Schwarzschild black holes moving through magnetic fields as unipolar inductors, predicting electromagnetic jet power and charge densities during mergers, with implications for electromagnetic counterparts to gravitational wave events.

Contribution

It introduces a novel framework for black holes acting as unipolar inductors, estimating electromagnetic power and charge distributions during mergers.

Findings

Black holes induce electric charge densities similar to pulsar magnetospheres.

Generated electromagnetic jets have power proportional to black hole mass and magnetic field strength.

Total energy loss includes contributions from both orbital motion and space-time rotation.

Abstract

(Abridged) The motion of a Schwarzschild black hole with velocity $v_0 = \beta_0 c$ through a constant magnetic field $B_0$ in vacuum induces a component of the electric field along the magnetic field, generating a non-zero second Poincare electromagnetic invariant $ ^* F \cdot F \neq 0$. This will produce (e.g., via radiative effects and vacuum breakdown) an electric charge density of the order of $\rho_{\rm ind}= B_0 \beta_0 /(2 \pi e R_G)$, where $R_G = 2 G M/c^2$ is the Schwarzschild radius and $M$ is the mass of the black hole; the charge density $\rho_{\rm ind}$ is similar to the Goldreich-Julian density. The magnetospheres of moving black holes resemble in many respects the magnetospheres of rotationally-powered pulsars, with pair formation fronts and outer gaps, where the sign of the induced charge changes. As a result, the black hole will generate bipolar electromagnetic jets each consisting of two counter-aligned current flows (four current flows total), each carrying an electric current of the order $I \approx e B_0 R_G \beta_0$. The electromagnetic power of the jets is $L \approx (G M)^2 B_0^2 \beta_0^2/c^3$; for a particular case of merging black holes the resulting Poynting power is $ L \approx {(G M)^3 B_0^2 /(c^5 R)}$, where $R$ is the radius of the orbit. In addition, in limited regions near the horizon the first electromagnetic invariant changes sign, so that the induced electric field becomes larger than the magnetic field, $E>B$. The total energy loss from a system of merging BHs is a sum of two components with similar powers, one due to the rotation of space-time within the orbit, driven by the non-zero angular momentum in the system, and the other due to the linear motion of the BHs through the magnetic field.