  Hawking radiation remains a crucial theoretical prediction of semi-classical
gravity and is considered one of the critical tests for a model of quantum
gravity. However, Hawking's original derivation used quantum field theory on a
fixed background. Efforts have been made to include the spacetime fluctuations
arising from the quantization of the dynamical degrees of freedom of gravity
itself and study the effects on the Hawking particles. Using semi-classical
analysis, we study the effects of quantum fluctuations of scalar field
stress-tensors in asymptotic non-flat spherically symmetric black-hole
space-times. Using two different approaches, we obtain a critical length-scale
from the horizon at which gravitational interactions become large, i.e., when
the back reaction to the metric due to the scalar field becomes significant.
For 4-D Schwarzschild AdS (SAdS) and Schwarzschild de Sitter (SdS), the number
of relevant modes for the back-reaction is finite only for a specific range of
values of M/L (where M is the mass of the black-hole, and L is related to the
modulus of the cosmological constant). For SAdS (SdS), the number of relevant
modes is infinite for M/L $\sim$ 1 (0.2 < M/L < $\frac{1}{3\sqrt{3}}$). We
discuss the implications of these results for the late stages of black-hole
evaporation.
