Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly

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 idea [17, 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 presence of gauge interactions. This was extended to conformal anomaly in [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 horizon [15, 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. Among the various approaches to derive Hawking radiation [1], two have recently stood apart in popularity: (i) the tunnelling mechanism by Parikh and Wilczek [2] and (ii) anomaly mechanism by Robinson and Wilczek [3]. Furthermore, there have been numerous refinements in the computational procedure [4]-[14]. Quite surprisingly, it seems that these two E-mail: [email protected]