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Hawking radiation due to photon and gravitino tunneling. (English) Zbl 1202.83077

Summary: Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking’s periodicity argument, the modified metric for the Schwarzschild black hole is given. This corrected version of the metric, up to \(\hbar \) order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.

MSC:

83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory
80A10 Classical and relativistic thermodynamics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81T20 Quantum field theory on curved space or space-time backgrounds
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