Nonradial Pulsation of General-Relativistic Stellar Models.IV. The Weakfield Limit
Abstract
In previous papers of this series techniques were developed for calculating the properties of the non- radial, quasi-normal pulsations of fully relativistic stellar models. In this paper those techniques are re- examined in the weak-field, nearly Newtonian limit, and are found to predict an emission of gravitational radiation at a rate which agrees with the standard weak-field approximation to general relativity. The present analysis also exhibits explicitly the radiation-reaction forces inside the star and shows that they sap pulsation energy from the star at the same rate as the waves carry it off. Following a train of ideas due to William L. Burke, the analysis is generalized to any weak-field, slow- motion system; and the relationship of the analysis to the post-Newtonian expansion schemes of Chandra- sekhar and Fock is discussed. It is shown that the dominant radiation-reaction forces associated with each changing multipole moment can be incorporated into Newtonian theory by a simple change in the boundary condition for the Newtonian potential at radial infinity
- Publication:
-
The Astrophysical Journal
- Pub Date:
- December 1969
- DOI:
- 10.1086/150259
- Bibcode:
- 1969ApJ...158..997T