Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation

Abstract

In this Letter we make a critique of, and comparison between, the anomaly method and WKB/tunneling method for obtaining radiation from non-trivial spacetime backgrounds. We focus on Rindler spacetime (the spacetime of an accelerating observer) and the associated Unruh radiation since this is the prototype of the phenomena of radiation from a spacetime, and it is the simplest model for making clear subtle points in the tunneling and anomaly methods. Our analysis leads to the following conclusions: (i) neither the consistent and covariant anomaly methods gives the correct Unruh temperature for Rindler spacetime and in some cases (e.g. de Sitter spacetime) the consistent and covariant methods disagree with one another; (ii) the tunneling method can be applied in all cases, but it has a previously unnoticed temporal contribution which must be accounted for in order to obtain the correct temperature.

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

“…Using the radial trajectory method, the tunneling research has been done in many cases including different black holes [9][10][11][12], different emitted particles [10][11][12][13][14] and cosmological horizons [13,15,16]. Also, using the Hamilton-Jacobi method, the tunneling analysis has been carried out and expanded, for example in Rindler spacetime [3,[17][18][19][20][21][22]. In these tunneling researches, the result that the tunneling probability is related to the change of Benkestein-Hawking (B-H) entropies before and after the emission are obtained.…”

Quantum tunneling from a high dimensional Gödel black hole

“…[51][52][53][54][55], the expression of the tunneling rate Γ ∝ exp −Im P dr , instead of Γ ∝ exp −2Im P dr is invariant under canonical transformations. So the fermion's tunneling rate of the five-dimensional Gödel black hole can be written as…”

Effects of quantum gravity on black holes

“…In section (2.3), the expression of the tunneling rate is not invariant under canonical transformations. To consider an invariance under canonical transformations, we follow the recent work [105,106,107] [105,106,107]. When this contribution is considered, the problem that there is a factor of two in the Hawking temperature would be resolved.…”