COMBINING THE TUNNELING AND ANOMALY PHENOMENA IN DERIVING THE GRAVITATIONAL ANOMALY

Abstract

In the present work we have derived the gravitational anomaly from a fundamentally different perspective: it emerges due to the tunneling of particles (in the present case fermions) across the black hole horizon. The latter effect is in fact the Hawking radiation. We have used the analogy of an early idea17,18 of visualizing chiral gauge anomaly as an effect of spectral flow of the energy levels, from the negative energy Dirac sea, across zero energy level in the presence of gauge interactions. This was extended to conformal anomaly in Ref. 23. 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. Furthermore, Hawking radiation induces a shrinking of the radius of the horizon15,16 which reminds us of a similar rearrangement in the Fermi level generated by the spectral flow.17,18,21 Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.