Kerr black-hole heat capacity at fixed angular momentum ($C_J$)

Writing $s=\sqrt{1-J^2/M^4}=\sqrt{1-a^2/M^2}$, the heat capacity of a Kerr black hole at fixed angular momentum isIt is positive for $\sqrt{2\sqrt{3}-3}<|a|/M<1$, diverges at the lower endpoint, and tends to zero in the extremal limit.