JTW > Research > The Quasi-Stationary Approach to the Binary Inspiral Problem
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You can now see my poster on this project from the 19th Texas Symposium on Relativistic Astrophysics. A project overview, contributed to the conference proceedings, can be found at gr-qc/9904010.

I am collaborating with William Krivan and Richard Price (Utah) and Joe Romano (Texas-Brownsville) on the problem of determining the rate and form of gravitational radiation emitted by two compact objects (such as black holes or neutron stars) orbiting one another in the strong-field regime. Such a binary system is stable in Newtonian gravity, but in GR the orbits will decay because gravitational radiation removes energy from the system. (This situation is of particular practical interest, since the gravitational radiation given off in the latter stages of such an inspiral is a prime candidate for detection by forthcoming gravitational wave observatories such as LIGO, VIRGO, and LISA.)

We are considering the regime where the gravitational interaction is too strong to use weak-field approximation methods, but the time scale for decay of the orbits is still long compared to the orbital period. In that regime, there should exist a solution describing non-decaying orbits in which a small amount of energy is somehow fed into the system to counteract the energy loss due to radiation. This reduces the numerical problem from dynamical evolution in four-dimensional spacetime to solution of the field equations on a three-dimensional space. To further simplify the numerical calculation while retaining many essential features of the actual problem, we will initially consider solutions which are also translationally invariant in the direction perpendicular to the orbital plane. (These solutions should describe the gravitational radiation emitted by a pair of orbiting cosmic strings.)

This project has naturally divided into several preliminary components:

I. Einstein equations for the two Killing vector spacetime (with Joe Romano) gr-qc/9812041; Phys Rev D 60, 084009 (1999)

Streamlining and generalizing the approach of Geroch [Phys Rev D 13, 394 (1972)] for treating four-dimensional spacetimes with two Killing vectors in terms of the two-dimensional space of Killing vector orbits, we determine the equations describing the metric for the co-rotating cosmic string problem in that form.

II. Radiation-balanced boundary conditions (with William Krivan and Richard Price) gr-qc/9909076; submitted to Classical and Quantum Gravity

In order for a co-rotating spacetime to be a solution of Einstein's equations, conservation of energy tells us it cannot have a net outward flux of gravitational wave energy. This work considers boundary conditions which replace the usual (causal) outgoing-wave form of a solution at infinity with a form containing equal amounts of incoming and outgoing radiation.

III. Gravitational radiation on a cylindrically-symmetric background

In a full 3+1 dimensional gravitational radiation problem, we could describe the waves, sufficiently far away, as perturbations to an asymptotically flat background. In the case of two orbiting cosmic strings, however, the infinite length precludes the existence of asymptotically flat regions of the spacetime, even in the transverse directions. A more reasonable background would then be that of a single line of mass (the Levi-Civita spacetime), so we should consider gravitational waves which are a perturbation to that background.

A seminar on this project is now available in online form from Penn State's relativity seminar page.