Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions

Journal of Mathematical Physics

Volumn 12, Issue 3, 1971, Pages 401-418

  Burke, William L ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b University of California Santa Cruz   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000989198     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1665603     Document Type: Article

References (44)

1. For more detail, see
2. The Equations of Motion
3. Gravitational Radiation in Ref. 2
4. Reference 1.
5. The singularity at [formula omitted] present in this example is not an essential feature of a “singular” problem.
6. Actually, we have here a very simple analog of the “Stokes’ paradox.” In 1851 Stokes proposed a simplified set of equations for viscous flow past a finite object, valid for the case of very low Reynold’s number. For 2-dimensional flow, all nontrivial solutions of Stokes’ equations diverge logarithmically at infinity. This “paradox” was resolved by Kaplun, who pointed out in 1954 that Stokes’ equations are only inner equations and their solutions are not valid far from the body.
7. The spurious solutions can be eliminated easily if the equations are solved by the method of two-time scales.
8. Runaway solutions also appear in some mechanical systems, for example, in the case of the spherically symmetric pulsations of a sphere which as a result radiates monopole sound waves. A more complete exposition of this material can be found
9. Conditions under which singular problems arise are discussed in M. Van Dyke
10. The Coupling of Gravitational Radiation to Non-Relativistic Sources
11. For these, see
12. This paper uses the sign conventions recommended by C. W. Misner, K. S. Thorne, and J. A. Wheeler (“Open Letter to Relativity Theorists,” August 19, 1968), with signature [formula omitted]
13. This κ is quite similar to the coupling parameter κ which appeared in the string problem.
14. We have, for example, [formula omitted] and will always take the contravariant components as our 3-vectors.
15. Since ρ is real we have [formula omitted] thus the F defined in Eq. (136) is real as is [formula omitted]
16. See, for example
17. Warning! Remember that we have calculated only the leading time-odd term in H. There are much larger time-even, post-Newtonian, and post-post-Newtonian corrections that have been ignored.
18. Ref. 32.
19. Use [formula omitted] and [formula omitted]