Entropy, topology of two-dimensional extreme black holes

TL;DR

This paper compares two treatments of entropy in two-dimensional extreme black holes, revealing different geometrical, topological, and quantum entropy properties, and suggests the existence of two distinct types of such black holes.

Contribution

It introduces a comparative analysis of Hawking's and Zaslavskii's treatments, highlighting their differing entropy calculations and topological implications for extreme black holes.

Findings

Different classical entropies arise from two treatments.

Distinct geometrical and topological properties are associated with each treatment.

Quantum entropies vary depending on the treatment and background.

Abstract

Through direct thermodynamic calculations we have shown that different classical entropies of two-dimensional extreme black holes appear due to two different treatments, namely Hawking's treatment and Zaslavskii's treatment. Geometrical and topological properties corresponding to these different treatments are investigated. Quantum entropies of the scalar fields on the backgrounds of these black holes concerning different treatments are also exhibited. Different results of entropy and geometry lead us to argue that there are two kinds of extreme black holes in the nature. Explanation of black hole phase transition has also been given from the quantum point of view.