### Abstract
:

Quantum gravity is one of the interesting fields in contemporary physics which is
still in progress. The purpose of quantum gravity is to present a quantum description
for spacetime at 10^-33cm or find the `quanta' of gravitational interaction.. At
present, the most viable theory to describe gravitational interaction is general relativity
which is a classical theory. Semi-classical quantum gravity or quantum field
theory in curved spacetime is an approximation to a full quantum theory of gravity.
This approximation considers gravity as a classical field and matter fields are
quantized. One interesting phenomena in semi-classical quantum gravity is Hawking
radiation. Hawking radiation was derived by Stephen Hawking as a thermal emission
of particles from the black hole horizon. In this thesis we obtain the spectrum of
Hawking radiation using a new method.
Vacuum is defined as the possible lowest energy state which is filled with pairs of
virtual particle-antiparticle. Vacuum polarization is a consequence of pair creation
in the presence of an external field such as an electromagnetic or gravitational field.
Vacuum polarization in the vicinity of a black hole horizon can be interpreted as
the cause of the emission from black holes known as Hawking radiation. In this
thesis we try to obtain the Hawking spectrum using this approach. We re-examine
vacuum polarization of a scalar field in a quasi-local volume that includes the horizon.
We study the interaction of a scalar field with the background gravitational field of
the black hole in the desired quasi-local region. The quasi-local volume is a hollow
cylinder enclosed by two membranes, one inside the horizon and one outside the
horizon. The net rate of particle emission can be obtained as the difference of the
vacuum polarization from the outer boundary and inner boundary of the cylinder.
Thus we found a new method to derive Hawking emission which is unitary and well
defined in quantum field theory.