Asymptotic tails of massive scalar fields in a Schwarzschild background

Hiroko Koyama; Akira Tomimatsu

doi:10.1103/PhysRevD.64.044014

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Asymptotic tails of massive scalar fields in a Schwarzschild background

Hiroko Koyama^* and Akira Tomimatsu^†

Department of Physics, Nagoya University, Nagoya 464-8602, Japan

^*Email address: hiroko@allegro.phys.nagoya-u.ac.jp
^†Email address: atomi@allegro.phys.nagoya-u.ac.jp

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Phys. Rev. D 64, 044014 – Published 26 July, 2001

DOI: https://doi.org/10.1103/PhysRevD.64.044014

Abstract

We investigate the asymptotic tail behavior of massive scalar fields in a Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of $t^{- 5 / 6}$ at asymptotically late times, and the oscillation with the period $2 π / m$ for the field mass m is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in a nearly extreme Reissner-Nordström background, which are discussed in terms of a resonant backscattering due to the space-time curvature.

References (14)

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[c1] R. Ruffini and J. A. Wheeler, Phys. Today 24, 30 (1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).

[c2] E. Poisson and W. Israel, Phys. Rev. D 41, 1796 (1990).

[c3] R. H. Price, Phys. Rev. D 5, 2419 (1972).

[c4] C. Gundlach, R. H. Price, and J. Pullin, Phys. Rev. D 49, 883 (1994).

[c5] C. Gundlach, R. H. Price, and J. Pullin, Phys. Rev. D 49, 890 (1994).

[c6] L. M. Burko and A. Ori, Phys. Rev. D 56, 7820 (1997).

[c7] L. Barack and A. Ori, Phys. Rev. Lett. 82, 4388 (1999).

[c8] H. Koyama and A. Tomimatsu, Phys. Rev. D 63, 064032 (2001).

[c9] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).

[c10] S. Hod and T. Piran, Phys. Rev. D 58, 044018 (1998).

[c11] L. M. Burko, in Abstracts of plenary talks and contributed papers of the “15th International Conference on General Relativity and Gravitation,” Pune, 1997, p. 143.

[c12] E. W. Leaver, Phys. Rev. D 34, 384 (1986).

[c13] Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1970).

[c14] A. Tomimatsu and H. Koyama, Phys. Rev. D 61, 124010 (2000).

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Asymptotic tails of massive scalar fields in a Schwarzschild background

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