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Creation of fermions at the charged black-hole horizon. (English) Zbl 0977.83045

From the author’s conclusion: We have considered a charged Dirac field outside a spherical charged star, stationary in the past and collapsing to a black hole in the future. The interaction between the field and the matter of the star is subsumed in a boundary condition belonging to a large class. We have rigorously established the famous result on the thermalization of the vacuum by the collapse: if the ground quantum state in the past is the Boulware vacuum, then this state becomes of Unruh type near the future black-hole horizon. Moreover the temperature and the chemical potential are independent of the history of the collapse and of the boundary condition (in the class that we introduced). A static observer at infinity interprets this state as a stream of particles and antiparticles outgoing from the black hole to infinity. Furthermore, the black-hole preferentially emits fermions whose charge is of same sign as its own charge, rather than fermions of opposite charge. We have investigated the rather subtle role of the cosmological constant in the case of the de Sitter-Reissner-Nordstrøm black-hole: in the case of a weakly charged black hole in an expanding universe, the temperature is an increasing function of the charge, unlike the asymptotically flat case; in the case of a strong charge, \(24M^2 < 25Q^2 < 25M^2\), the temperature is an increasing function of the cosmological constant. We have only studied the two-point function which carries the information on the vacuum fluctuations.

MSC:

83C57 Black holes
81T20 Quantum field theory on curved space or space-time backgrounds
83C22 Einstein-Maxwell equations
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