The Hawking effect for spin 1/2 fields
The author proves the validity of the Hawking effect for a gravitational collapse of a charged star in the presence of a charged massive Dirac field. The paper represents a development of a work by \textit{J. Dimock} and \textit{B. S. Kay} [``Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric. I.'', Ann. Phys. 175, 366--426 (1987; Zbl 0628.53080)], as well as that by \textit{A. Bachelot} [``The Hawking effect'', Ann. Inst. Henri Poincaré, Phys. Théor. 70, No. 1, 41--99 (1999; Zbl 0919.53034)]. In the last paper one uses the Fock vacuum for both scalar and Dirac quanta. The aim of the present paper is to prove the Hawking effect for a charged Dirac field from the point of view of a fixed observer in Schwarzschild variables for a collapsing charged star. More precisely, in this work F. Melnyk considers a very simplified model of a gravitational collapse of a star modelled by a reflecting sphere. The author chooses the MIT bag boundary condition [\textit{A. Chodos} et al., Phys. Rev. D (3) 9, 3471--3495 (1974)], which causes the reflection of the fields on the star surface analogously as it occurs for a bosonic field by using a Dirichlet condition. The author supposes that the spherical symmetry is preserved during the collapse, such that the De Sitter-Reissner-Nordström metric is not changing during the collapse. The collapse occurs in the Fock vacuum. Although this last assumption is not physically correct in the case of De Sitter-Reissner-Nordstrom space-time, the mathematical proof remains valid. In this case it would be preferable to consider a thermal state whose temperature is that of Gibbons-Hawking associated to a cosmological horizon. A lack of the paper consists in the neglecting of bound states for massive particles, which were examined for some particular cases in: \textit{I. M. Ternov, A. B. Gaina} and \textit{G. A. Chizhov}, ``Finite motion of electrons in the field of microscopic black holes'', Sov. Phys. J. 23, No. 8, 695--700 (1980; Zbl 1043.83543); \textit{D. V. Gal'tsov} and \textit{A. A. Ershov}, ``Fermion bound states in the Kerr-Newman field with magnetic charge'', Moscow Univ. Phys. Bull. 42, 33--38 (1987); \textit{A. Lasenby, C. Doran, J. Pritchard} and \textit{A. Caceres}, ``Bound states and Decay times of fermions in a Schwarzschild black hole background'' (2000) e-print Archive: gr-qc/0209090.
scientific article; zbMATH DE number 2034805