Thermodynamics of Gauss-Bonnet black holes revisited

We investigate the Gauss-Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss-Bonnet coupling c and mass M, comparing with those of the Born-Infeld-AdS (BIAdS), Reissner-Norstrom-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c < 0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c > 0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c 0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.