Hawking radiation as tunneling from the Kerr and Kerr-Newman black holes

Abstract

Recent work, which treats the Hawking radiation as a semi-classical tunneling process at the horizon of the Schwarzschild and Reissner-Nordström spacetimes, indicates that the exact radiant spectrum is no longer pure thermal after considering the black hole background as dynamical and the conservation of energy. In this paper, we extend the method to investigate Hawking radiation as massless particles tunneling across the event horizon of the Kerr black hole and that of charged particles from the Kerr-Newman black hole by taking into account the energy conservation, the angular momentum conservation, and the electric charge conservation. Our results show that when self-gravitation is considered, the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum, but is consistent with an underlying unitary theory.

Quantum tunneling beyond semiclassical approximation

“…[7]. Later, many people [8] used the radial null geodesic method to find out the Hawking temperature for different spacetime metrics. Recently [9], tunneling of a Dirac particle through the event horizon was also studied.…”

Charged fermions tunnelling from Kerr–Newman black holes

“…Tunnelling provides not only a useful verification of thermodynamic properties of black holes but also an alternate conceptual means for understanding the underlying physical process of black hole radiation. For scalar field emission it has been shown to be very robust, having been successfully applied to a wide variety of interesting and exotic spacetimes, including the Kerr and Kerr-Newman cases [10,11,14], black rings [12], the 3-dimensional BTZ black hole [7,13], the Vaidya spacetime [18], other dynamical black holes [19], Taub-NUT spacetimes [14], Gödel spacetimes [22], and dynamical horizons [19]. Tunnelling methods have even been applied to horizons that are not black hole horizons including those with cosmological horizons [5], [6], [25],and Rindler Spacetimes [4], [14], [24] for which it has been shown the Unruh temperature [30] is in fact recovered.…”

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

“…The first law can be interpreted as the relationship among the global charges, parameters (M, e, J) and T, S which is obtained by performing a variation of the Euclidean action resulting from perturbing the location of the inner and outer horizons. Viewing the Hawking radiation and emission of particles as a quantum tunneling that shrinks the size of the horizons [25] is another way of perturbing the value of the Euclidean action. For a thorough discussion of interpreting Einstein's field equations as just a thermo-dynamical equation of state see [26] and Wald's entropy expression related to the global Noether charge of diffs under the Killing vector field which generates the event horizon in the stationary black hole background and which is given by a local geometric density integrated over a space-like section of the horizon [39].…”

“…If one views the Hawking emission of particles as a tunneling phenomenon through the horizon [25], when there are two horizon solutions to the transcendental equation (2.11) one may compute the Euclidean Einstein-Hilbert action in the bounded domain determined by the outer and inner horizons r ± (σ) defined by :…”