Scattering of scalar fields by spherical gravitational collapse. (English) Zbl 0872.53066

The paper studies by a precise mathematical analysis the scattering of classical scalar fields by black-hole information. The main point of interest is the infinite Doppler effect measured by an observer at rest in Schwarzschild coordinates. The functional framework associated with this phenomenon is constructed. The existence and strong asymptotic completeness of the wave operators are proven.


53Z05 Applications of differential geometry to physics
83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory
Full Text: DOI


[1] Bachelot, A., Gravitational scattering of electromagnetic field by Schwarzschild Black-Hole, Ann. Inst. Henri Poincaré, Physique théorique, 54, 3, 261-320 (1991) · Zbl 0743.53037
[2] Bachelot, A., Asymptotic completeness for the Klein-Gordon Equation on the Schwarzschild metric, Ann. Inst. Henri Poincaré, Physique théorique, 61, 4, 411-441 (1994) · Zbl 0809.35141
[3] Bachelot, A.; Motet-Bachelot, A., Les résonances d’un trou noir de Schwarzschild, Ann. Inst. Henri Poincaré, Physique théorique, 59, 1, 3-68 (1993) · Zbl 0793.53094
[4] Birrel, N. D.; Davies, P. C.W., Quantum fields in curved space (1982), Cambridge University Press · Zbl 0476.53017
[5] Choquet-Bruhat, Y., Hyperbolic partial differential equation on a manifold, (de Witt, Wheeler, Battelle rencontres (1967), Benjamin: Benjamin New York) · Zbl 0169.43202
[6] Christodoulou, D., The formation of black-holes and singularities in spherically gravitational collapse, Comm. Pure Appl. Math., 44, 339-373 (1991) · Zbl 0728.53061
[7] Dimock, J., Scattering for the wave equation on the Schwarzschild metric, Gen. Rel. Grav., 17, 4, 353-369 (1985) · Zbl 0618.35088
[8] Dimock, J.; Kay, B. S., Scattering for massive scalar fields or Coulomb potentials and Schwarzschild metrics, class. Quantum Grav., 3, 71-80 (1986) · Zbl 0591.35080
[9] Fredenhagen, K.; Haag, R., On the derivation of Hawking radiation associated with the formation of a black-hole, Commun. Math. Phys., 127, 273-284 (1990) · Zbl 0692.53040
[10] Hawking, S., Particle creation by black holes, Commun. Math. Phys., 43, 199-220 (1975) · Zbl 1378.83040
[11] Hörmander, L., The analysis of linear partial differential operators III (1985), Springer-Verlag · Zbl 0601.35001
[12] Nicolas, J.-P., Scattering of linear Dirac fields by a spherically symetric black-hole, Ann. Inst. Henri Poincaré, Physique théorique, 62, 2, 145-179 (1995) · Zbl 0826.53072
[13] Nicolas, J.-P., Non linear Klein-Gordon equation on Schwarzschild-like metrics, J. Math. Pures Appl., 74, 35-58 (1995) · Zbl 0853.35123
[14] Petkov, V., Scattering theory for hyperbolic operators (1989), North-Holland · Zbl 0687.35067
[15] Reed, M.; Simon, B., (Methods of modern mathematical physics, Vol. II, III (1978), Academic Press) · Zbl 0401.47001
[16] Wald, R., On particle creation by black-holes, Commun. Math. Phys., 45, 9-34 (1975)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.