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

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