Quantum entropy of two-dimensional extreme charged dilaton black hole

TL;DR

This paper compares classical and quantum entropy calculations for two-dimensional extreme charged dilaton black holes using different methods, revealing a new divergence in quantum entropy linked to phase transitions.

Contribution

It introduces a new divergent term in quantum entropy under the extreme limit and explores its connection with phase transitions.

Findings

A divergence appears in quantum entropy at the extreme limit.

Different methods yield distinct entropy values.

The divergence is related to phase transition phenomena.

Abstract

By using Hawking's treatment as well as Zaslavskii's treatment respectively and the brick wall model, two different values of classical entropy and quantum entropy of scalar fields in the two-dimensional extreme charged dilaton black hole backgrounds have been obtained. A new divergent term emerges in the quantum entropy under the extreme limit for Zaslavskii's treatment and its connection with the phase transition has been addressed.