Kerr black-hole heat capacity at fixed angular momentum
= Kerr black-hole heat capacity at fixed angular momentum
{c}
{title2=$C_J$}
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 is
$$
C_J=4\pi M^2\frac{s(1+s)}{2-2s-s^2}.
$$
It is positive for $\sqrt{2\sqrt3-3}<|a|/M<1$, diverges at the lower endpoint, and tends to zero in the extremal limit.