  We employ a recently developed mode-sum regularization method to compute the
renormalized stress-energy tensor of a quantum field in the Kerr background
metric (describing a stationary spinning black hole). More specifically, we
consider a minimally-coupled massless scalar field in the Unruh vacuum state,
the quantum state corresponding to an evaporating black hole. The computation
is done here for the case $a=0.7M$, using two different variants of the method:
$t$-splitting and $\varphi$-splitting, yielding good agreement between the two
(in the domain where both are applicable). We briefly discuss possible
implications of the results for computing semiclassical corrections to certain
quantities, and also for simulating dynamical evaporation of a spinning black
hole.
