Fermions’ Tunnelling from the Reissner- Nordström-Anti-de Sitter Black Hole

Very recent work of Kerner and Mann involving fermions tunnelling from the Rindler space-time and a general non-rotating black hole is extended to the case of Reissner-Nordström-anti-de Sitter black hole. Due to the couple between the gravity field and electromagnetic field, we introduce the Dirac equation of the charged particles to determine the action of the radiation. We further consider the correction of the thermal spectrum in the unfixed background space time. It is shown that when the energy and charge conservations are considered, the tunnelling rate of fermions is also related to the change of Bekenstein-Hawking entropy, implying the underlying unitary theory is satisfied.