$ds^2 = -\left(1-\frac{2GM}{c^2r}\right)c^2dt^2 + \frac{dr^2}{1-\frac{2GM}{c^2r}} + r^2d\theta^2 + r^2\sin^2\theta d\phi^2$

$ds^2 = -\frac{\Delta - a^2\sin^2\theta}{\rho^2}c^2dt^2 + \frac{4GMar\sin^2\theta}{c\rho^2}dtd\phi + \frac{\rho^2}{\Delta}dr^2 + \rho^2d\theta^2 + \frac{\sin^2\theta}{\rho^2}[(r^2+a^2)^2 - a^2\Delta\sin^2\theta]d\phi^2$

$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}$

$T_H = \frac{\hbar c^3}{8\pi G M k_B}$
$\frac{dM}{dt} = -\frac{\hbar c^4}{15360\pi G^2 M^2}$

$S_{BH} = \frac{k_B c^3 A}{4\hbar G} = \frac{k_B c^3}{4\hbar G} \cdot 4\pi r_s^2 = \frac{\pi k_B c^3}{G\hbar}r_s^2$