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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., Published in Physical Review D: http://link.aps.org/doi/10.1103/PhysRevD.88.064059

A near-equal mass binary black hole can clear a central cavity in a circumbinary accretion disk; however, previous works have revealed accretion streams entering this cavity. Here we use 2D hydrodynamical simulations to study the accretion streams and their periodic behavior. In particular, we perform a suite of simulations, covering different binary mass ratios $q=M_2/M_1$ in the range $0.01 \leq q \leq 1$. In each case, we follow the system for several thousand binary orbits, until it relaxes to a stable accretion pattern. We find the following results: (i) while the binary is efficient in maintaining a low-density cavity, the time-averaged mass accretion rate into the cavity, through narrow coherent accretion streams, is suppressed by at most a factor of $\sim 5$, compared to a disk with a single BH with the same mass; (ii) the largest suppression occurs for $q\approx 0.05$; binaries whose mass ratios are either lower or higher both suppress accretion less significantly; (iii) for $q \gtrsim 0.05$, the accretion rate is strongly modulated by the binary, and depending on the precise value of $q$, the power spectrum of the accretion rate shows either one, two, or three distinct periods; and (v) for $q \lesssim 0.05$, the accretion rate becomes steady, with no time-variations. Most binaries produced in galactic mergers are expected to have $q\gtrsim 0.05$. If the luminosity of these binaries tracks their accretion rate, then a periodogram of their light-curve could help in their identification, and to constrain their mass ratio and disk properties., Published in MNRAS