  This thesis is focussed towards the applications of the quantum tunneling
mechanism to study black holes. Here we give a general frame work of the
existing tunneling mechanism, both the radial null geodesic and Hamilton Jacobi
methods. On the radial null geodesic method side, we study the modifications to
the tunneling rate, Hawking temperature and the Bekenstein- Hawking area law by
including the back reaction as well as non-commutative effects in the
space-time. A reformulation of the Hamilton-Jacobi (HJ) method is first
introduced. Based on this, a close connection between the quantum tunneling and
the gravitational anomaly mechanisms to discuss Hawking effect, is put
forwarded. An interesting advantage of this reformulated HJ method is that one
can get directly the emission spectrum from the event horizon of the black
hole, which was missing in the earlier literature. Also, the quantization of
the entropy and area of a black hole is discussed in this method. Another part
of the thesis is the introduction of a new type of global embedding of curved
space-time to higher dimensional Minkowskian space-time (GEMS). Using this a
unified description of the Hawking and Unruh effects is given. Advantage of
this approach is, it simplifies as well as generalises the conventional
embedding. In addition to the spherically symmetric space-times, the
Kerr-Newman black hole is exemplified. Finally, following the above ideas and
the definition of partition function for gravity, it is shown that
extremization of entropy leads to the Einstein's equations of motion. In this
frame work, a relation between the entropy, energy and the temperature of a
black hole is given where energy is shown to be the Komar expression.
Interestingly, this relation is the generalized Smarr formula. In this
analysis, the GEMS method provides the law of equipartition of energy as an
intermediate step.
