Thermodynamics of de Sitter black holes with a conformally coupled scalar field

TL;DR

This paper investigates the thermodynamics of de Sitter black holes with a conformally coupled scalar field, focusing on their entropy, temperature, and horizon energies, and how these are affected by the scalar field and charge.

Contribution

It introduces a detailed analysis of the thermodynamics of lukewarm Reissner-Nordstrom-de Sitter black holes with a conformally coupled scalar field, including modifications to entropy and horizon energies.

Findings

Entropy is modified by the scalar field's non-minimal coupling.

The Euclidean action approach is adapted for charged cases.

The first law from the isolated horizons formalism yields horizon energies.

Abstract

We study the thermodynamics of de Sitter black holes with a conformally coupled scalar field. The geometry is that of the ``lukewarm'' Reissner-Nordstrom-de Sitter black holes, with the event and cosmological horizons at the same temperature. This means that the region between the event and cosmological horizons can form a regular Euclidean instanton. The entropy is modified by the non-minimal coupling of the scalar field to the geometry, but can still be derived from the Euclidean action, provided suitable modifications are made to deal with the electrically charged case. We use the first law as derived from the isolated horizons formalism to compute the local horizon energies for the event and cosmological horizons.