Saturation of Pauli blocking in near-extremal charged Nariai black holes

We solve the Dirac equation for a massive charged fermion in the near-extremal charged Nariai black hole with the near-horizon geometry <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>dS</a:mi> <a:mn>2</a:mn> </a:msub> <a:mo>×</a:mo> <a:msup> <a:mi mathvariant="normal">S</a:mi> <a:mn>2</a:mn> </a:msup> </a:math> . At the one-loop level, contrary to the catastrophic emission of charged spinless bosons in C.-M. Chen , [], we show that the emission of fermions in a narrow timelike inner region between the cosmological horizon and black hole horizon saturates the bound from the Pauli blocking and does not give an amplification (quantum superradiance). Using the reciprocal relation, we find the Schwinger emission of fermions from <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>AdS</d:mi> <d:mn>2</d:mn> </d:msub> <d:mo>×</d:mo> <d:msup> <d:mi mathvariant="normal">S</d:mi> <d:mn>2</d:mn> </d:msup> </d:math> , and compare the Schwinger emission of fermions and bosons from near-extremal Nariai black holes.