×

Scattering for the wave equation on the Schwarzschild metric. (English) Zbl 0618.35088

The scattering problem for the massless scalar field in Schwarzschild’s space-time is studied at length. Special (tortoise) coordinates are used, in which the horizon is placed at infinity. This implies that the wave operator has to be constructed in two distinct asymptotic domains, namely the horizon and the Minkowski regions of space-time. The existence of the wave operator follows from the adaption of the existence theorem for a general class of asymptotically flat space-times.
Reviewer: M.Maia

MSC:

35P25 Scattering theory for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Dimock, J., and Kay, B. Scattering for scalar fields on Coulomb potentials and Schwarzschild metrics (to appear). · Zbl 0659.53054
[2] Dimock, J., and Kay, B. Scattering for scalar quantum fields on black hole metrics (to appear). · Zbl 0591.35080
[3] Dimock, J., and Kay, B. (1982).,Ann. Inst. Henri Poincaré,37, 93-114.
[4] Kato, T. (1970).J. Functional Analysis,1, 342-369. · Zbl 0171.12303
[5] Reed, M., and B. Simon, (1977).Math. Z.,155, 163-180. · Zbl 0346.35081
[6] Reed, M., and Simon, B. (1979).Methods of Modern Mathematical Physics, Vol. III (Academic Press, New York). · Zbl 0405.47007
[7] Kato, T. (1966).Perturbation Theory for Linear Operators (Springer-Verlag, New York). · Zbl 0148.12601
[8] Reed, M., and Simon, B. (1975).Methods of Modern Mathematical Physics, Vol. II (Academic Press, New York). · Zbl 0308.47002
[9] Reed, M., and Simon, B. (1978).Methods of Modern Mathematical Physics, Vol. IV (Academic Press, New York). · Zbl 0401.47001
[10] Beig, R. (1982).Acta Phys. Austr.,54, 129.
[11] Davies, E. B., and Simon, B. (1978).Commun. Math. Phys.,63, 277-301. · Zbl 0393.34015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.