Daniel Kennefick

The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary’s accumulated orbital phase can be measured to a fractional accuracy ≪10^-3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves’ information, but is not necessary for wave detection.

Superradiance-tidal friction correspondence

Since the work of Hartle in the 1970s, and the subsequent development of the the Membrane Paradigm approach to black hole physics it has been widely accepted that superradiant scattering of gravitational waves bears strong similarities with the phenomenon of ``tidal friction (well-known from Newtonian gravity) operating in binary systems of viscous material bodies. In this paper we revisit the superradiance-tidal friction analogy within the context of ultracompact relativistic bodies. We advocate that as long as these bodies have non-zero viscosity they should undergo tidal friction that can be construed as a kind of superradiant scattering from the point of view of the dynamics of an orbiting test-body. In addition we consider the presence of anisotropic matter, which is required for at least some ultracompact bodies, if they are to sustain a radius very close to the gravitational radius. We find that the tidal friction/superradiance output is enhanced with increasing anisotropy and that strongly anisotropic systems exhibit an unconventional response to tidal and centrifugal forces. Finally, we make contact with the artificial system comprising a black hole with its horizon replaced by a mirror (sometimes used as a proxy for ultracompact material bodies) and discuss superradiance and tidal friction in relation to it.

Do floating orbits in extreme mass ratio binary black holes exist

This paper examines the possibility of floating or non-decaying orbits for extreme mass ratio binary black holes. In the adiabatic approximation, valid in the extreme mass ratio case, if the orbital flux lost due to gravitational radiation reaction is compensated for by the orbital flux gained from the spins of the black holes via superradiant scattering (or, equivalently, tidal acceleration) the orbital decay would be stalled, causing the binary to float. We show that this flux balance is not, in practice, possible for extreme mass ratio binary black holes with circular equatorial orbits; furthermore, adding eccentricity and inclination to the orbits will not significantly change this null result, thus ruling out the possibility of floating orbits for extreme mass ratio binary black holes. We also argue that binaries consisting of material bodies dense and massive enough to generate gravitational waves detectable by any kind of gravitational wave detector are also unlikely to float. Using a multipolar analysis, we show that a non-Kerr spacetime which could produce a floating orbit (given the same amount of tidal acceleration as in the case of a Kerr black hole) would need to be rapidly rotating prolate spheroid, which would be an exotic object indeed.

Darboux transformation in black hole perturbation theory

The Darboux transformation between ordinary differential equations is a 19th century technique that has seen wide use in quantum theory for producing exactly solvable potentials for the Schrodinger equation with specific spectral properties. In this paper we show that the same transformation appears in black hole theory, relating, for instance, the Zerilli and Regge-Wheeler equations for axial and polar Schwarzschild perturbations. The transformation reveals these two equations to be isospectral, a well known result whose method has been repeatedly reintroduced under different names. We highlight the key role that the so-called algebraically special solutions play in the black hole Darboux theory and show that a similar relation exists between the Chandrasekhar-Detweiler equations for Kerr perturbations. Finally, we discuss the limitations of the method when dealing with long-range potentials and explore the possibilities offered by a generalised Darboux transformation.