Thermodynamics of Gauss-Bonnet black holes revisited

Understand

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-Norstr\"om-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 pseudo-charge.