On 4D Hawking radiation from the effective action

Abstract

We determine the s-waves contribution of a scalar field to the four dimensional effective action for arbitrary spherically symmetric external gravitational fields. The result is applied to 4d-black holes and it is shown that the energy momentum tensor derived from the (nonlocal) effective action contains the Hawking radiation. The luminosity is close to the expected one in the s-channel. The energy momentum tensor may be used as starting point to study the backreaction problem.

Hawking radiation by effective two-dimensional theories

“…This makes the trace anomaly to differ from eq. (2.7) by extra φ terms [15], [16], [17], [18], [19] 5) which is still state independent. The coefficient of the last term in eq.…”

“…Unfortunately, for the Schwarzschild space-time the T ab so deduced is not even in qualitative agreement with the 4D T µν : it predicts a negative (!) Hawking flux for an evaporating black hole [15], [18]. This fact shades serious doubts on the validity of this more "sophisticated" (as compard to eq.…”

“…Puzzled with this problem, the authors of Ref. [15] proposed to add Weyl invariant nonlocal terms to the above effective action S aind . The resulting T ab has the desired feature for a Schwarzschild black hole and correctly reproduces the Hawking flux at infinity.…”

Dilaton gravity in two dimensions

“…The first calculation of the conformal anomaly for non-minimally coupled scalar fields with the spherically reduced path integral measure (Ψ = Φ) has been presented by Mukhanov, Wipf and Zelnikov [333] who were also the first to address the problem of Hawking radiation for spherically reduced matter.…”

“…[333,102,226]. Different expressions for the conformal anomaly with various choices of the measure were reported too [48,342,325,343].…”