Thermodynamical, geometrical and Poincaré methods for charged black holes in presence of quintessence

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.