Scattering of massless scalar waves by a Schwarzschild " singularity"

Richard A. Matzner

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78 Citations (Scopus)

Abstract

This paper investigates the scattering and absorption of scalar waves satisfying the equation φ = 0 in the Schwarzschild metric. This problem has been previously considered by Hildreth. We find, for a Schwarzschild mass m, the following cross sections in the zero-frequency limit for s-waves: σ(absorption) = 0, dσ/dΩ ≃ [c + 1/3(2m) ln (2mω)]2, where c is a constant of order m. These results disagree with the previous calculation. We exhibit a method of solution for the equation. Its limiting (Newtonian) form, with suitable identification of the coefficients, is the problem of Coulomb scattering in non-relativistic quantum mechanics. By demanding coordinate conditions which for large l allow the usual Coulomb results in a partial-wave expansion, we are able to define a partial-wave cross section. The (summed) differential cross section for small frequencies inherits the logarithmic behavior of the s-wave part, which is the only contribution explicitly calculated. (The l ≠ 0 contributions and the behavior of the cross sections for ω ≠ 0 are qualitatively indicated.) Cosmological considerations are given which cut off this divergence.

Original languageEnglish (US)
Pages (from-to)163-170
Number of pages8
JournalJournal of Mathematical Physics
Volume9
Issue number1
DOIs
StatePublished - Jan 1 1968

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Scattering
Scalar
Singularity
scalars
Cross section
cross sections
scattering
Schwarzschild metric
Absorption
Partial
elastic waves
quantum mechanics
divergence
cut-off
Quantum Mechanics
Divergence
Logarithmic
Limiting
coefficients
Metric

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Scattering of massless scalar waves by a Schwarzschild " singularity". / Matzner, Richard A.

In: Journal of Mathematical Physics, Vol. 9, No. 1, 01.01.1968, p. 163-170.

Research output: Contribution to journalArticle

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