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.

Recently, it has been shown that the radiation arising from quantum fields placed in a gravitational background (e.g. Hawking radiation) can be derived using a quasi-classical calculation. Here we show that this method has a previously overlooked temporal contribution to the quasi-classical amplitude. The source of this temporal contribution lies in different character of time in general relativity versus quantum mechanics. Only when one takes into account this temporal contribution does one obtain the canonical temperature for the radiation. Although in this letter the specific example of radiation in de Sitter space-time is used, the temporal contribution is a general contribution to the radiation given off by any gravitational background where the time coordinate changes its signature upon crossing a horizon. Thus, the quasi-classical method for gravitational backgrounds contains subtleties not found in the usual quantum mechanical tunneling problem.

We present a simple and general procedure for calculating the thermal radiation coming from any stationary metric. The physical picture is that the radiation arises as the quasi-classical tunneling of particles through a gravitational barrier. We study three cases in detail: the linear accelerating observer (Unruh radiation), the non-rotating black hole (Hawking radiation), and the rotating/orbiting observer (circular Unruh radiation). For the linear accelerating observer we obtain a thermal spectrum with the usual Unruh temperature. For the non-rotating black hole we obtain a thermal spectrum, but with a temperature twice that given by the original Hawking calculations. We discuss possible reasons for the discrepancies in temperatures as given by the two different methods. For the rotating/orbiting case the quasi-classical tunneling approach indicates that there is no thermal radiation. This result for the rotating/orbiting case has experimental implications for the experimental detection of this effect via the polarization of particles in storage rings.

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.

Unruh radiation is the thermal flux seen by an accelerated observer moving through Minkowski spacetime. In this article we study Unruh radiation as tunneling through a barrier. We use a WKB-like method to obtain the tunneling rate and the temperature of the Unruh radiation. This derivation brings together many topics into a single problem -classical mechanics, relativity, relativistic field theory, quantum mechanics, thermodynamics and mathematical physics. Moreover, this gravitational WKB method helps to highlight the following subtle points: (i) the tunneling rate strictly should be written as the closed path integral of the canonical momentum; (ii) for the case of the gravitational WKB problem, there is a time-like contribution to the tunneling rate arising from an imaginary change of the time coordinate upon crossing the horizon. This temporal contribution to the tunneling rate has no analog in the ordinary quantum mechanical WKB calculation.