Big black hole, little neutron star: Magnetic dipole fields in the Rindler spacetime
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 an electromagnetic counterpart to gravitational-wave detection, a black hole battery is of more general interest as a novel luminous astrophysical source. 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_⊙ 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 bursts, jets, beamed radiation, or even a hot spot on the neutron star crust.