The Coupling of Gravitational Radiation to Nonrelativistic Sources

Citation

Burke, William Lionel (1969) The Coupling of Gravitational Radiation to Nonrelativistic Sources. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/89HA-6J10. https://resolver.caltech.edu/CaltechETD:etd-10152002-090530

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis examines the problem of the coupling of gravitational radiation to its sources in the limit of weak fields and slowly-moving sources; it shows in detail how the irreversibility caused by the escape of radiation can be included in the formalism. The usual slow-motion expansions of General Relativity (EIH and post-Newtonian) have the difficulty that they are not uniformly valid for large distances - distances where radiation becomes important and where the outgoing wave-boundary condition must be imposed. This difficulty is eliminated by using the method of matched asymptotic expansions. A second asymptotic expansion, in the same slowness parameter as enters in the near zone, is used to represent the radiation. This outer expansion provides matching conditions on the inner expansion that generate radiative corrections to the inner expansion. Using this technique we show that the escape of radiation leads to an extraction of energy from the sources, without ever having to define the energy carried in the gravitational waves. The damping is found by calculating the work done by the fields that react back on the source. Explicit expressions are given for these fields, and these can be used to calculate, in lowest order, all the irreversible effects caused by radiation. In this thesis the problem of calculating radiation reaction for bodies with very weak gravitational fields (U/c[superscript 2] << v[superscript 2]/c[superscript 2] << 1) is solved definitely. The case of gravitationally bound systems (U/c[superscript 2] [...] v[superscript 2/c[superscript 2] << 1) is discussed and a program for dealing with this case is set up, but the calculations for this case have not yet been done.

Thesis Files