Nonanalytic terms in the slow-motion expansion of a radiating scalar field on a Schwarzschild background

Details Nonanalytic terms in the slow-motion expansion of a radiating scalar field on a Schwarzschild background Nonanalytic terms in the slow-motion expansion of a radiating scalar field on a Schwarzschild background

Apr 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phrvd..25.2030k&link_type=abstract

Physical Review D (Particles and Fields), Volume 25, Issue 8, 15 April 1982, pp.2030-2037

Physics

7

Scientific paper

We demonstrate that when slow-motion infinities arise in an assumed power-series expansion of a time-varying scalar field, they signal the occurrence of terms of logarithmic order in the slow-motion expansion parameter. Previous approximation techniques used in general relativity have assumed that all quantities could be expanded in powers of the small parameter(s). This paper provides the first example, within general relativity, of perturbative effects whose order of magnitude is not a power, but a nonanalytic function of a small parameter. Several previous slow-motion derivations of gravitational radiation damping contained divergent integrals. We first show how an inappropriate expansion method produces divergent integrals in scalar perturbations on a Schwarzschild background. We then use matched asymptotic expansions to discover the aforementioned logarithmic terms. We employ the method of strained coordinates to seek a wave-zone expansion that is uniformly valid at very large distances. We also find that an unexpectedly large, time-odd term in the near zone, which arises via matching to the lowest wave-zone order, is canceled when higher wave-zone orders are considered. No divergent integrals occur. These same techniques will be used in a future paper on the much more complicated gravitational problem.

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