Black holes, brick walls and the Boulware state

TL;DR

This paper re-evaluates the brick-wall model for black hole entropy, clarifying that previous concerns about its self-consistency are unfounded when correctly identifying the Boulware state, and discusses its relation to the Gibbons-Hawking instanton.

Contribution

It demonstrates that the brick-wall model and Gibbons-Hawking instanton are mutually exclusive but complementary descriptions of black hole entropy.

Findings

Reservations about the model's self-consistency are unfounded.

Correct identification of the Boulware state resolves issues.

The two models are mutually exclusive but complementary.

Abstract

The brick-wall model seeks to explain the Bekenstein-Hawking entropy as a wall-contribution to the thermal energy of ambient quantum fields raised to the Hawking temperature. Reservations have been expressed concerning the self-consistency of this model. For example, it predicts large thermal energy densities near the wall, producing a substantial mass-correction and, presumably, a large gravitational back-reaction. We re-examine this model and conclude that these reservations are unfounded once the ground state---the Boulware state---is correctly identified. We argue that the brick-wall model and the Gibbons-Hawking instanton (which ascribes a topological origin to the Bekenstein-Hawking entropy) are mutually exclusive, alternative descriptions (complementary in the sense of Bohr) of the same physics.