Subtleties in the Quasi-Classical Calculation of Hawking Radiation

Abstract

The quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.

Quantum tunneling beyond semiclassical approximation

“…This indicates that 't' coordinate has an imaginary part for the crossing of the horizon of the black hole and correspondingly there will be a temporal contribution to the probabilities for the ingoing and outgoing particles. This has similarity with [16] where they show for the Schwarzschild metric that two patches across the horizon are connected by a discrete imaginary amount of time.…”

“…From the above one can easily show that Im t = −2πM for the Schwarzschild spacetime which is precisely the imaginary part of the transformation t → t − 2iπM when one connects the two regions across the horizon as shown in [16]. Therefore the probability of the outgoing particle is…”

“…Our approach, on the other hand, is similar to in spirit [16] where it has been shown that 't' changes by an imaginary discrete amount across the horizon. Indeed, the explicit expression for this change, in the case of Schwarzschild metric, calculated from our general formula (3.16) agrees with the findings of [16].…”

Black holes and black hole thermodynamics without event horizons

“…Since the expansion of the null generators is positive or zero, the infinitesimal area must increase or stay the same by equation (1). Since the null generator lies in the horizon, the total area of the horizon can be found by integrating (1) over the choice of foliation of the horizon.…”

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…”