Canonical stability of a Schwarzschild--anti-de Sitter black hole (Canonical stability of a Schwarzschild-AdS black hole)

The Schwarzschild--anti-de Sitter heat capacity has the sign of $d{T}_H/d{r}_{+}$. It is positive precisely for $r_{+}>L/\sqrt{3}$, so these large black holes are locally stable in a fixed-temperature reservoir.