Hawking radiation in a non-covariant frame: the Jacobi metric approach
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, 700108, Kolkata, India
2 Department of Physics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India
Accepted: 13 August 2020
Published online: 18 August 2020
The present paper deals with a reformulation of the derivation of Hawking temperature for static and stationary black holes. In contrast to the conventional approach, where the covariant form of the metrics is used, we use the manifestly non-covariant Jacobi metric for the black holes in question. In the latter, a restricted form of Hamilton–Jacobi variational principle is exploited where the energy of the particle (pertaining to Hawking radiation) appears explicitly in the metric as a constant parameter. Our analysis shows that, as far as computation of Hawking temperature (for stationary black holes) is concerned, the Jacobi metric framework is more streamlined and yields the result with less amount of complications (as for example, considerations of positive and negative energy modes and signature change of the metric across horizon do not play any direct role in the present analysis).
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