Big Black Hole, Little Neutron Star: Magnetic Dipole Fields in the Rindler Spacetime

TL;DR

This paper derives exact analytic solutions for electromagnetic fields of a magnetic dipole near a black hole horizon, revealing potential electromagnetic signals from black hole-neutron star mergers that could serve as observable counterparts to gravitational waves.

Contribution

It provides the first exact solutions for magnetic dipoles in Rindler spacetime and analyzes the electromagnetic power output during black hole-neutron star inspiral.

Findings

Voltage up to ~10^16 statvolts generated by the black hole battery.

Projected luminosity of about 10^42 ergs/s for typical parameters.

Larger black holes produce less electromagnetic power at fixed gravitational radii.

Abstract

As a black hole and neutron star approach during inspiral, the field lines of a magnetized neutron star eventually thread the black hole event horizon and a short-lived electromagnetic circuit is established. The black hole acts as a battery that provides power to the circuit, thereby lighting up the pair just before merger. Although originally suggested as a promising electromagnetic counterpart to gravitational-wave detection, the luminous signals are promising more generally as potentially detectable phenomena, such as short gamma-ray bursts. To aid in the theoretical understanding, we present analytic solutions for the electromagnetic fields of a magnetic dipole in the presence of an event horizon. In the limit that the neutron star is very close to a Schwarzschild horizon, the Rindler limit, we can solve Maxwell's equations exactly for a magnetic dipole on an arbitrary worldline. We present these solutions here and investigate a proxy for a small segment of the neutron star orbit around a big black hole. We find that the voltage the black hole battery can provide is in the range ~10^16 statvolts with a projected luminosity of 10^42 ergs/s for an M=10M_sun black hole, a neutron star with a B-field of 10^12 G, and an orbital velocity ~0.5c at a distance of 3M from the horizon. Larger black holes provide less power for binary separations at a fixed number of gravitational radii. The black hole/neutron star system therefore has a significant power supply to light up various elements in the circuit possibly powering jets, beamed radiation, or even a hot spot on the neutron star crust.