Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly

Abstract

We investigate the phase transitions of black holes with conformal anomaly in canonical ensemble from different perspectives. Some interesting and novel phase transition phenomena have been discovered. Firstly, we discuss the behavior of the specific heat and the inverse of the isothermal compressibility. It is shown that there are striking differences in Hawking temperature and phase structure between black holes with conformal anomaly and those without it. In the case with conformal anomaly, there exists local minimum temperature corresponding to the phase transition point. Phase transitions take place not only from an unstable large black hole to a locally stable medium black hole but also from an unstable medium black hole to a locally stable small black hole. Secondly, we probe in details the dependence of phase transitions on the choice of parameters. The results show that black holes with conformal anomaly have much richer phase structure than those without it. There would be two, only one or no phase transition points depending on the parameters we have chosen. The corresponding parameter region are derived both numerically and graphically. Thirdly, geometrothermodynamics are built up to examine the phase structure we have discovered. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges. Furthermore, critical behaviors are investigated by calculating the relevant critical exponents. It is proved that these critical exponents satisfy the thermodynamic scaling laws, leading to the conclusion that critical exponents and the scaling laws can reserve even when we consider conformal anomaly.

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• Thermogeometric phase transition in a unified framework
• Phase transition and critical phenomena of black holes: A general approach
• A general framework to study the extremal phase transition of black holes
• Thermogeometric study of van der Waals like phase transition in black holes: an alternative approach
• The intrinsic curvature of thermodynamic potentials for black holes with critical points
• Phantom black holes and critical phenomena
• A consistent and unified picture for critical phenomena of $f(R)$ AdS black holes
• Testing thermodynamic laws and weak cosmic censorship conjecture of conformal anomaly corrected AdS black hole