Entropy Function and Universal Entropy of Two-Dimensional Extremal Black Holes

TL;DR

This paper derives the entropy of two-dimensional extremal black holes using the entropy function approach, demonstrating its universality and proportionality to the dilaton field at the horizon, even with higher derivative corrections.

Contribution

It shows that the entropy of 2D extremal black holes is universal and proportional to the dilaton at the horizon, including higher derivative effects, unifying previous results.

Findings

Entropy is proportional to the dilaton at the horizon.

Universality of entropy holds even with higher derivative terms.

Results agree with previous literature on 2D dilaton gravity.

Abstract

The entropy for two-dimensional black holes is obtained through the entropy function with the condition that the geometry approaches an $AdS_2$ spacetime in the near horizon limit. It is shown that the entropy is universal and proportional to the value of the dilaton field at the event horizon as expected. We find this universal behavior holds even after the inclusion of higher derivative terms, only modifying the proportional constant. More specifically, a variety of models of the dilaton gravity in two dimensions are considered, in which it is shown that the universal entropy coincides with the well-known results in the previous literatures.