Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly

In this Letter we have derived the gravitational anomaly leading to the Hawking radiation from a fundamentally different perspective: it emerges due to the {\it{complimentary}} roles played by tunneling and (gravitational) anomaly. We have used the analogy of an early idea \cite{niel1} of visualizing chiral gauge anomaly as an effect of {\it{spectral flow}} of the energy levels, from the negative energy Dirac sea, across zero energy level in presence of gauge interactions. This was extended to conformal anomaly in \cite{fumita}. In the present work, we exploit the latter formalism in black hole physics where we interpret crossing the horizon of black hole (the zero energy level) as a spectral flow since it is also accompanied by a change of sign in the energy of the particle. Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.

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