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Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times as that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed.
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Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy momentum tensor, occur in two different forms -- covariant and consistent. The crucial role of covariant anomalies near the horizon is revealed since this is the {it only} input required to obtain the Hawking flux, thereby highlighting the universality of this effect. A brief description to apply this method to obtain thermodynamic entities like entropy or temperature is provided.
We comment on the consistence of the epsilon anti-symmetric tensor adopted in [R. Banerjee and S. Kulkarni, arXiv:0707.2449] when it is generalized in the general case where $sqrt{-g} eq 1$. It is pointed out that the correct non-minimal consistent gauge and gravitational anomalies should by multiplied a factor $sqrt{-g} eq 1$. We also sketch the generalization of their work to the $sqrt{-g} eq 1$ case.
We extend the work by S. Iso, H. Umetsu and F. Wilczek [Phys. Rev. Lett. 96 (2006) 151302] to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole space-time with the determinant of its diagonal metric differing from the unity ($sqrt{-g} eq 1$) and use it to investigate Hawking radiation from the Reissner-Nordstrom black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy momentum and gauge fluxes required to cancel gravitational and gauge anomalies at the horizon are precisely equivalent to the $(1+1)$-dimensional thermal fluxes associated with Hawking radiation emanating from the horizon at the Hawking temperature. These fluxes are universally determined by the value of anomalies at the horizon.
Hawking radiation is obtained from the Reissner-Nordstr{o}m blackhole with a global monopole and the Garfinkle-Horowitz-Strominger blackhole falling in the class of the most general spherically symmetric blackholes $(sqrt{-g} eq1)$, using only chiral anomaly near the event horizon and covariant boundary condition at the event horizon. The approach differs from the anomaly cancellation approach since apart from the covariant boundary condition, the chiral anomaly near the horizon is the only input to derive the Hawking flux.
Hawking radiation of the blackhole is calculated based on the principle of local field theory. In our approach, the radiation is a unitary process, therefore no information loss will be recorded. In fact, observers in different regions of the space communicate using the Hawking radiation, when the systems in the different regions are entangled with each other. The entanglement entropy of the blackhole is also calculated in the local field theory. We found that the entanglement entropy of the systems separated by the blackhole horizon is closely connected to the Hawking radiation in our approach. Our calculation shows that the entanglement entropy of the systems separated by the horizon of a blackhole is just a pure number $frac{pi^3 + 270 zeta(3)}{360 pi^2}$, independent of any parameter of the blackhole, and its relation to the Hawking radiation is given by $S_{EE} = frac{8 pi}{3} frac{pi^3 + 270 zeta(3)}{pi^3 + 240 zeta(3)} {cal A} R_H$, where $S_{EE}$ is the entanglement entropy, $cal A$ is the area of the horizon, and $R_H$ is the Hawking radiation.
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