Hawking radiation as tunneling with back-reaction for the Kerr-anti-de Sitter black hole

Medved and Vagenas demonstrated how the Angheben-Nadalini-Vanzo-Zerbini analysis can be adapted in describing the effects of the gravitational back-reaction for the generic spherically symmetric black hole. We extend the Medved-Vagenas quantum tunneling method to the case of the stationary axisymmetric Kerr black hole in anti-de Sitter space-times. We find a correction to the Hawking radiation by considering the effects of the gravitational back-reaction and also energy conservation and angular momentum conservation.