Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

Abstract:We give a correction to the tunneling probability by taking into account the back reaction effect to the metric of the black hole spacetime. We then show how this gives rise to the modifications in the semiclassical black hole entropy and Hawking temperature. Finally, we reproduce the familiar logarithmic correction to the Bekenstein-Hawking area law.In 1975, Hawking discovered [1] the remarkable fact that black holes, previously thought to be completely black regions of spacetime from which nothing can escape, actually radiate a thermal spectrum of paticles and that the temperature of this radiation depends on the surface gravity of the black hole by the relation T H = K 0 2π . This discovery was consistent with an earlier discovery [2, 3, 4, 5] of a connection between black holes and thermodynamics which revealed that the entropy of a black hole is proportional to the surface area of its horizon, S BH = A 4 . From this, using the second law of thermodynamics dM = T H dS BH , the temperature of the black hole can be calculated. This is actually due to an analogy between the second law of thermodynamics and the black hole equation dM = K 0 8π dA. These relations are all based on classical or semiclassical considerations.It is possible to include quantum effects in this discussion of Hawking radiation. Using the conformal anomaly method the modifications to the spacetime metric by the one loop back reaction was computed [6,7]. Later it was shown [8,9] that the Bekenstein-Hawking area law was modified, in the leading order, by logarithmic corrections. Similar conclusions were also obtained by using quantum gravity techniques [10,11,12]. Likewise, corrections to the semiclassical Hawking temperature were derived [7,8].A particularly useful and intuitive way to understand the Hawking effect is through the tunneling formalism as developed in [13]. The semiclassical Hawking temperature is very simply and quickly obtained [13,14] in this scheme by exploiting the form of the semiclassical tunneling rate. A natural question that arises in this context is the feasibility of this approach to include quantum corrections. Although there have been sporadic attempts [15,16] a systematic, thorough and complete analysis is still lacking.In this paper we compute the corrections to the semiclassical tunneling rate by including the effects of self gravitation and back reaction. The usual expression found in [13], given in the Maxwell-Boltzmann form e − E T BH , is modified by a prefactor. This prefactor leads to a modified Bekenstein-Hawking entropy. The semiclassical Bekenstein-Hawking area law connecting the entropy to the horizon area is altered. As obtained in other approaches [9,10,12], the leading correction is found to be logarithmic while the nonleading one is a series in inverse powers *

We obtain, using a reformulation of the tunneling mechanism, the Hawking black body spectrum with the appropriate temperature for a black hole. This is a new result in the tunneling formalism of discussing Hawking effect. Our results are given for a spherically symmetric geometry that is asymptotically flat.Comment: LaTex, 6 pages, no figures, minor modifications, to appear in Phys. Lett.

Generalizing the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.

Abstract:We give a general derivation, for any static spherically symmetric metric, of the relation T h = K 2π connecting the black hole temperature (T h ) with the surface gravity (K), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and back reaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one. IntroductionClassical general relativity gives the concept of black hole from which nothing can escape. This picture was changed dramatically when Hawking[1] incorporated the quantum nature into this classical problem. In fact he showed that black hole radiates a spectrum of particles which is quite analogous with a thermal black body radiation. Thus Hawking radiation emerges as a nontrivial consequence of combining gravity and quantum mechanics.After his original derivation which was based on the calculation of Bogoliubov coefficients in the asymptotic states, Hawking together with Hartle[2] gave a simpler, path integral derivation. Physically, black hole radiation can be interpreted as the quantum tunneling of vacuum fluctuations through the horizon. This picture was mathematically formulated in [3]. An important step of this method is the calculation of tunneling amplitude from which the Hawking temperature is obtained. This is done either by using the trajectory of a null geodesic [3] or by solving the Hamilton-Jacobi equation to calculate the imaginary part of the action variable [4].The tunneling approach was subsequently used to compute the Hawking temperature for black holes with different types of metric [5]. The results have agreed with the general *