Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly

TL;DR

This paper presents a novel derivation of the gravitational anomaly responsible for Hawking radiation by combining tunneling effects and anomaly phenomena, using spectral flow analogy in black hole physics.

Contribution

It introduces a new perspective by linking tunneling and gravitational anomaly through spectral flow, offering a different derivation of the gravitational anomaly in black hole physics.

Findings

Successfully derived the gravitational anomaly from the combined tunneling and anomaly approach.

Connected the spectral flow concept to black hole horizon crossing.

Provided insights into the origin of Hawking radiation via this novel framework.

Abstract

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.