  It is believed that extremal black holes do not emit Hawking radiation as
understood by taking extremal limits of non-extremal black holes. However, it
is debated whether one can make such conclusion reliably starting from an
extremal black hole, as the associated Bogoliubov coefficients which relate
ingoing and outgoing field modes do not satisfy the required consistency
condition. We address this issue in a canonical approach firstly by presenting
an exact canonical derivation of the Hawking effect for non-extremal Kerr black
holes. Subsequently, for extremal Kerr black holes we show that the required
consistency condition is satisfied in the canonical derivation and it produces
zero number density for Hawking particles. We also point out the reason behind
the reported failure of Bogoliubov coefficients to satisfy the required
condition.

General Relativity and Quantum Cosmology;High Energy Physics - Theory