Thermodynamical, geometrical and Poincar\'e methods for charged black holes in presence of quintessence

TL;DR

This paper investigates the thermodynamical stability, phase transitions, and geometric properties of charged black holes surrounded by quintessence, using classical thermodynamics, Poincaré methods, and geometric approaches.

Contribution

It introduces a comprehensive analysis combining thermodynamical, geometrical, and Poincaré methods to study stability and phase transitions of charged black holes with quintessence.

Findings

Limits for entropy, temperature, and potential for stability identified.

Microcanonical ensembles are shown to be stable.

Different geometric methods agree on phase transition points.

Abstract

Properties pertaining to thermodynamical local stability of Reissner-Nordstr\"om black holes surrounded by quintessence as well as adiabatic invariance, adiabatic charging and a generalized Smarr formula are discussed. Limits for the entropy, temperature and electric potential ensuring stability of canonical ensembles are determined by the classical thermodynamical and Poincar\'e methods. By the latter approach we show that microcanonical ensembles (isolated black holes) are stable. Two geometrical approaches lead to determine the same states corresponding to second order phase transitions.