Energy Momentum Tensor of the Evaporating Black Hole and Local Bogoljubov Transformations

TL;DR

This paper generalizes Hawking's method of black hole evaporation using local Bogoljubov transformations, revealing a local energy flux with partial thermal features and quantum interference effects that diminish with distance.

Contribution

It introduces a local approach to black hole evaporation, expressing the energy-momentum tensor in terms of local inertial modes and revealing partial thermal behavior.

Findings

Local energy flux exhibits partial thermal character.

Quantum interference effects are present and diminish with distance.

The method provides a local perspective on black hole radiation.

Abstract

The method of Hawking to obtain black hole evaporation through Bogoljubov transformation between asymptotic modes (in and out) is generalized. The construction is local in that the in modes (of say positive frequency) are decomposed by Bogoljubov transformation into positive and negative frequency local inertial modes (i.e. those which are solutions of the d'Alembertian in terms of the local normal coordinates). From this follows an interesting reexpression of the local energy momentum tensor, more particularly of the outgoing energy flux. One finds that even in the local description there exists a partial thermal character parametrized by a local temperature. There exists quantum interference effects as well. These become negligible at large distance from the black hole.