Hawking temperature in the tunneling picture

Abstract

We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, Γ ∝ exp(Im[ p dr]), rather than, Γ ∝ exp(2Im[ p dr]), for the tunneling probability/decay rate one obtains twice the original Hawking temperature. The former expression for Γ is argued to be correct since p dr is invariant under canonical transformations, while p dr is not. Thus, either the tunneling methods of calculating Hawking radiation are suspect or the Hawking temperature is twice that originally calculated.

Quantum tunneling beyond semiclassical approximation

“…Here also the Hawking temperature is explicitly calculated which exactly matches with that evaluated in Schwarzschild like coordinates. In all these cases there is no ambiguity regarding a factor of two in the temperature, as reported in [15,18,34,35].…”

Hawking radiation as quantum tunneling in Rindler coordinate

“…It was pointed out that this approach to the tunneling interpretation of Hawking radiation has ambiguities such coordinatedependence of the Hawking temperature and non-invariance of the action under canonical transformations [37], [38].…”

“…In fact, the ambiguity of the temperature is originated from the coordinate used to calculate the emission rate. Another ambiguity is that the action (5), in particular, the imaginary part is not invariant under canonical transformations [37], [38].…”

“…In refs. [37] and [38] the emission rate was suggested as a contour integral, which makes the rate invariant under canonical transformations.…”

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…”