# Kerr black hole evaporation time question

Is there any closed (even if complicated) formula por the Hawking evaporation time for a Kerr black hole (and more general black holes) just like the one $$$$t_e=\dfrac{5120\pi G^2M_0^3}{\hbar c^4}$$$$ for Schwarzschild black hole? Any reference about those? I am writing a black hole vademecum document I will post in a weeks worldwide and I need those formulae... Remark: I presume that, in the Kerr black hole formula $$T_{BH}(Kerr)=\dfrac{\hbar c^3}{4\pi GMk_B}\left(\dfrac{\sqrt{\dfrac{G^2M^2}{c^4}-\dfrac{J^2}{c^2M^2}}}{\dfrac{GM}{c^2}+\sqrt{\dfrac{G^2M^2}{c^4}-\dfrac{J^2}{c^2M^2}}}\right)=\dfrac{\hbar c^3}{4\pi GMk_B}\left(\dfrac{\sqrt{1-a^2}}{1+\sqrt{1-a^2}}\right)$$ both mass $$M$$ and $$a$$ are varying (or $$M,J$$). So, I believe it is no so easy to calculate the evaporation time for Kerr black holes. Anyway, if someone knows references about that, I would also be pleased.

• That formula for the Schwarzschild hole is an approximation that neglects so-called gray-body factors. – G. Smith Jul 12 '20 at 16:35