Steven L. Detweiler

Pulsar timing measurements and the search for gravitational waves

Pulse arrival time measurements of pulsars may be used to search for gravitational waves with periods on the order of 1 to 10 years and dimensionless amplitudes approx.10/sup -11/. The analysis of published data on pulsar regularity sets an upper limit to the energy density of a stochastic background of gravitational waves, with periods approx.1 year, which is comparable to the closure density of the universe.

Spherically symmetric solutions in five-dimensional general relativity

The most general time-independent spherically symmetric (in the usual three space dimensions) solution to the five-dimensional vacuum Einstein equations is found, subject to the existence of a Killing vector in the fifth direction. The significance of these solutions is discussed within the context of a previously proposed extension of the Kaluza-Klein model in which the universe, although (4+1)-dimensional, has evolved over cosmic times into an effectively (3+l)-dimensional one.

Black holes and gravitational waves. III. The resonant frequencies of rotating holes

The free oscillations of rotating black holes are studied. Values of the complex resonant frequencies are given as functions of the Kerr parameter a for a variety of spherical harmonic indices l and m. The Appendix uses analytic methods to show that the maximally rotating Kerr solution is, in some sense, marginally unstable.

Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry

A small mass {mu} in orbit about a much more massive black hole m moves along a world line that deviates from a geodesic of the black hole geometry by O({mu}/m). This deviation is said to be caused by the gravitational self-force of the metric perturbation h{sub ab} from {mu}. For circular orbits about a nonrotating black hole we numerically calculate the O({mu}/m) effects upon the orbital frequency and upon the rate of passage of proper time on the world line. These two effects are independent of the choice of gauge for h{sub ab} and are observable in principle. For distant orbits, our numerical results agree with a post-Newtonian analysis including terms of order (v/c){sup 6}.

High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

We continue a previous work on the comparison between the post-Newtonian (PN) approximation and the gravitational self-force (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We nd that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coecients. Using standard PN theory we compute analytically the leading 4PN and the next-to-leading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF results support well the analytic PN calculations through rst order in the mass ratio, and are used to accurately measure the 4PN and 5PN non-logarithmic coecients in a particular gauge invariant observable. Furthermore we are able to give estimates of higher order contributions up to the 7PN level. We also conrm with high precision the value of the 3PN

Perspective on gravitational self-force analyses

A point particle of mass μ moving on a geodesic creates a perturbation hab, of the spacetime metric gab, that diverges at the particle. Simple expressions are given for the singular μ/r part of hab and its tidal distortion caused by the spacetime. This singular part hSab is described in different coordinate systems and in different gauges. Subtracting hSab from hab leaves a regular remainder hRab. The self-force on the particle from its own gravitational field adjusts the worldline at O(μ) to be a geodesic of gab + hRab; this adjustment includes all of the effects of radiation reaction. For the case that the particle is a small non-rotating black hole, we give a uniformly valid approximation to a solution of the Einstein equations, with a remainder of O(μ2) as μ → 0. An example presents the actual steps involved in a self-force calculation. Gauge freedom introduces ambiguity in perturbation analysis. However, physically interesting problems avoid this ambiguity.

Low multipole contributions to the gravitational self-force

We calculate the unregularized monopole and dipole contributions to the self-force acting on a particle of small mass in a circular orbit around a Schwarzschild black hole. From a self-force point of view, these nonradiating modes are as important as the radiating modes with

On the secular instabilities of the Maclaurin spheroids

lg~2.

Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results

In fact, we demonstrate how the dipole self-force contributes to the dynamics even at the Newtonian level. The self-acceleration of a particle is an inherently gauge-dependent concept, but the Lorenz gauge is often preferred because of its hyperbolic wave operator. Our results are in the Lorenz gauge and are also obtained in closed form, except for the even-parity dipole case where we formulate and implement a numerical approach.

Self-force of a scalar field for circular orbits about a Schwarzschild black hole

The combined effects of gravitational radiation reaction and of viscosity on the stability of the Maclaurin spheroids are discussed. Each of these dissipative effects is known to induce a secular instability in the Maclaurin sequence past the point of bifurcation of the Jacobi and the Dedekind sequences. We find, however, that when both effects are considered together, these instabilities tend to cancel each other. The sequence of stable Maclaurin spheroids therefore reaches past the bifurcation point to a new point determined by the ratio of the strengths of the viscous and the radiative forces.