Alan G. Wiseman

Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order

The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order O[(Gm/rc 2 ) 2 ] beyond the quadrupole approximation. The result has been derived by two independent calculations of the (source) multipole moments. The 2PN terms, and in particular the finite mass contribution therein (which cannot be obtained in perturbation calculations of black hole spacetimes), are shown to make a significant contribution to the accumulated phase of theoretical templates to be used in matched filtering of the data from future gravitational-wave detectors.

Self-force on a static scalar test charge outside a Schwarzschild black hole

The finite part of the self-force on a static scalar test-charge outside a Schwarzschild black hole is zero. By direct construction of Hadamards elementary solution, we obtain a closed-form expression for the minimally coupled scalar field produced by a test-charge held fixed in Schwarzschild spacetime. Using the closed-form expression, we compute the necessary external force required to hold the charge stationary. Although the energy associated with the scalar field contributes to the renormalized mass of the particle (and thereby its weight), we find there is no additional self-force acting on the charge. This result is unlike the analogous electrostatic result, where, after a similar mass renormalization, there remains a finite repulsive self-force acting on a static electric test-charge outside a Schwarzschild black hole. We confirm our force calculation using Carters mass-variation theorem for black holes. The primary motivation for this calculation is to develop techniques and formalism for computing all forces - dissipative and non-dissipative - acting on charges and masses moving in a black-hole spacetime. In the Appendix we recap the derivation of the closed-form electrostatic potential. We also show how the closed-form expressions for the fields are related to the infinite series solutions.

Upper limits on gravitational-wave signals based on loudest events

Searches for gravitational-wave bursts have often focused on the loudest event(s) in searching for detections and in determining upper limits on astrophysical populations. Typical upper limits have been reported on event rates and event amplitudes which can then be translated into constraints on astrophysical populations. We describe the mathematical construction of such upper limits.

Coalescing binary systems of compact objects to (post)5/2-Newtonian order. IV. The gravitational wave tail.

The contribution to gravitational radiation from the gravitational wave «tail» is studied using an expression previously obtained by Blanchet and Damour. The expression for the tail of the radiation contains integrals over the past history of the system, thus exhibiting the backscattering nature of radiation in curved spacetime; however the dependence on the remote past of the system is shown to be weak for relevant astrophysical systems. In the cases of circular orbits and high-speed, low-deflection (bremsstrahlung) encounters, the integrals can be evaluated analytically. For circular orbits the frequency of the tail radiation is twice the orbital frequency, just as for the quadrupole radiation, but is phase shifted from it

Finding Fields and Self-Force in a Gauge Appropriate to Separable Wave Equations

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a radiation gauge. The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component {psi}{sub 0} (or {psi}{sub 4}) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but {psi}{sub 0} and {psi}{sub 4} are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin {+-}2 parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related morexa0» to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized {psi}{sub 0} (or {psi}{sub 4}) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge. «xa0less

A matched expansion approach to practical self-force calculations

We discuss a practical method of computing the self-force on a particle moving through a curved spacetime. This method involves two expansions to calculate the self-force, one arising from the particles immediate past and the other from the more distant past. The expansion in the immediate past is a covariant Taylor series and can be carried out for all geometries. The more distant expansion is a mode sum, and may be carried out in those cases where the wave equation for the field mediating the self-force admits a mode expansion of the solution. In particular, this method can be used to calculate the gravitational self-force for a particle of mass μ orbiting a black hole of mass M to order μ2, provided μ/M 1. We discuss how to use these two expansions to construct a full self-force, and in particular investigate criteria for matching the two expansions. As with all methods of computing self-forces for particles moving in black hole spacetimes, one encounters considerable technical difficulty in applying this method; nevertheless, it appears that the convergence of each series is good enough that a practical implementation may be plausible.

The self-force on a non-minimally coupled static scalar charge outside a Schwarzschild black hole

The finite part of the self-force on a static, non-minimally coupled scalar test charge outside a Schwarzschild black hole is zero. This result is determined from the work required to slowly raise or lower the charge through an infinitesimal distance. Unlike similar force calculations for minimally-coupled scalar charges or electric charges, we find that we must account for a flux of field energy that passes through the horizon and changes the mass and area of the black hole when the charge is displaced. This occurs even for an arbitrarily slow displacement of the non-minimally coupled scalar charge. For a positive coupling constant, the area of the hole increases when the charge is lowered and decreases when the charge is raised. The fact that the self-force vanishes for a static, non-minimally coupled scalar charge in Schwarzschild spacetime agrees with a simple prediction of the Quinn–Wald axioms. However, Zelnikov and Frolov computed a non-vanishing self-force for a non-minimally coupled charge. Our method of calculation closely parallels the derivation of Zelnikov and Frolov, and we show that their omission of this unusual flux is responsible for their (incorrect) result. When the flux is accounted for, the self-force vanishes. This correction eliminates a potential counter example to the Quinn–Wald axioms. The fact that the area of the black hole changes when the charge is displaced brings up two interesting questions that did not arise in similar calculations for static electric charges and minimally coupled scalar charges. (1) How can we reconcile a decrease in the area of the black hole horizon with the area theorem which concludes that δAreahorizon ≥ 0? The key hypothesis of the area theorem is that the stress–energy tensor must satisfy a null-energy condition Tαβlαlβ ≥ 0 for any null vector lα. We explicitly show that the stress–energy associated with a non-minimally coupled field does not satisfy this condition, and this violation of the hypothesis leads directly to the decreasing area. (2) Since the entropy of a Schwarzschild black hole is proportional to the area of the horizon, and the area of the horizon will change while we slowly raise or lower the charge, we must ask: does this simple process conserve entropy? The process does conserve entropy; however, the appropriate entropy for a gravitational theory with a non-minimally coupled scalar field is the Iyer–Wald generalized entropy which—in addition to the area of the black hole—includes a contribution from the scalar field evaluated on the horizon. We explicitly calculate the generalized entropy of a Schwarzschild black hole bathed in the field of a static, non-minimally coupled scalar test charge, and show that it is conserved when the charge is slowly raised or lowered.

Self-force on an accelerated particle

We calculate the singular field of an accelerated point particle (scalar charge, electric charge or small gravitating mass) moving on an accelerated (nongeodesic) trajectory in a generic background spacetime. Using a mode-sum regularization scheme, we obtain explicit expressions for the self-force regularization parameters. We use a Lorentz gauge for the electromangetic and gravitational cases. This work extends the work of Barack and Ori [1] who demonstrated that the regularization parameters for a point particle in geodesic motion in a Schwarzschild spacetime can be described solely by the leading and subleading terms in the mode-sum (commonly known as the

Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes

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Coalescing binary systems of compact objects to (post)5/2-Newtonian order. III. Transition from inspiral to plunge.

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