  It is well known that extremal black holes do not Hawking radiate, which is
usually realized by taking an extremal limit from the nonextremal case.
However, one cannot perceive the same phenomenon using the Bogoliubov
transformation method starting from an extremal black hole itself, i.e.,
without the limiting case consideration. In that case, the Bogoliubov
coefficients do not satisfy the required normalization condition. In canonical
formulation, which closely mimics the Bogoliubov transformation method, one can
consistently reproduce the vanishing number density of Hawking quanta for an
extremal Kerr black hole. In this method, the relation between the spatial
near-null coordinates, imperative in understanding the Hawking effect, was
approximated into a sum of linear and inverse terms only. In the present work,
we first show that one can reach the same conclusion in canonical formulation
even with the complete relationship between the near-null coordinates, which
contains an additional logarithmic term. It is worth mentioning that in the
nonextremal case, a similar logarithmic term alone leads to the thermal Hawking
radiation. Secondly, we study the case with only the inverse term in the
relation (i.e., when the spatial near-null coordinates associated to the past
and future observers are inversely related to each other) to understand whether
it is the main contributing term in vanishing number density. Third, for a
qualitative realization, we consider a simple thought experiment to understand
the corresponding Hawking temperature and conclude that the inverse term indeed
plays a crucial role in the vanishing number density.
