A note on Hawking radiation via complex path analysis

Details A note on Hawking radiation via complex path analysis A note on Hawking radiation via complex path analysis

2009-11-24

arxiv.org/abs/0911.4574v2

Class. Quantum Grav. 27 (2010) 205013

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, v2; manuscript divided into sections, many discussions and references added

Scientific paper

10.1088/0264-9381/27/20/205013

As long as we neglect backreaction, the Hawking temperature of a given black hole would not depend upon the parameters of the particle species we are considering. In the semiclassical complex path analysis approach of Hawking radiation, this has been verified by taking scalar and Dirac spinors separately for different stationary spacetime metrics. Here we show, in a coordinate independent way that, for an arbitrary spacetime with any number of dimensions, the equations of motion for a Dirac spinor, a vector, spin-$2$ and spin-$\frac{3}{2}$ fields reduce to Klein-Gordon equations in the WKB semiclassical limit. We then obtain, under some suitable assumptions, the complex solutions of those resulting scalar equations across the Killing horizon of a stationary spacetime to get a coordinate independent expression for the emission probability identical for all particle species. Finally we consider some explicit examples to demonstrate the validity of that expression.

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