Non-thermal Hawking radiation from the Kerr black hole

We present a short and direct derivation of Hawking radiation by using the Damour-Ruffini method, as taking into account the self-gravitational interaction from the Kerr black hole. It is found that the radiation is not exactly thermal, and because the derivation obeys conservation laws, the non-thermal Hawking radiation can carry information from the black hole. So it can be used to explain the black hole information paradox, and the process satisfies unitary.