Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0897.53064
Bachelot, Alain
Quantum vacuum polarization at the black-hole horizon. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 67, No.2, 181-222 (1997). ISSN 0246-0211

This paper is inspired by previous work of {\it J. Dimock} and {\it B. S. Kay} [Ann. Phys. 175, 366-426 (1987; Zbl 0628.53080) and J. Math. Phys. 27, 2520-2525 (1986; Zbl 0608.53065)] where the Hawking effect is treated by algebraic scattering theory on the external Schwarzschild solution. In the present paper the same problem is considered on a spacetime containing a collapsing star. The fundamental difference between the two approaches concerns the treatment of the classical field equations. Since the spacetime region exterior to the collapsing star is not globally hyperbolic, we need boundary conditions on the surface of the star to get unique solutions of the Cauchy problem. Therefore the major part of this paper is concerned with the treatment of this mixed, i.e., intial and boundary value problem. The corresponding dicussion follows very closely previous work of the author [{\it A. Bachelot}, J. Math. Pures Appl., IX. Ser. 76, 155-210 (1997; Zbl 0872.53066)] which considers classical wave scattering on the same class of spacetimes. The only difference to the present paper is the usage of another Sobolev class for the initial data ($H^1 \times L^2$ instead of $H^{1/2} \times H^{-1/2}$ which is used in the paper under review). The discussion of the quantum part differs from the paper of Dimock and Kay cited above only by the fact that the asymptotic in-region consists, due to the lack of the past horizon, only of lightlike past infinity.
[M.Keyl (Berlin)]

MSC 2000:: *53Z05 Appl. of differential geometry to physics
83C57 Black holes
81T20 Quantum field theory on curved space backgrounds
58J45 Hyperbolic equations
58J32 Boundary value problems on manifolds

Keywords: Hawking effect; collapsing star; classical field equations; Cauchy problem

Citations: Zbl 0628.53080; Zbl 0608.53065; Zbl 0872.53066

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]