  From Einstein's theory we know that besides the electromagnetic spectrum,
objects like quasars, active galactic nuclei, pulsars and black holes also
generate a physical signal of purely gravitational nature. The actual form of
the signal is impossible to determine analytically, which lead to use of
numerical methods.
  Two major approaches emerged. The first one formulates the gravitational
radiation problem as a standard Cauchy initial value problem, while the other
approach uses a Characteristic Initial value formulation. In the strong field
region, where caustics in the wavefronts are likely to form, the Cauchy
formulation is more advantageous. On the other side, the Characteristic
formulation is uniquely suited to study radiation problems because it describes
space-time in terms of radiation wavefronts.
  The fact that the advantages and disadvantages of these two systems are
complementary suggests that one may want to use the two of them together. In a
full nonlinear problem it would be advantageous to evolve the inner (strong
field) region using Cauchy evolution and the outer (radiation) region with the
Characteristic approach. Cauchy Characteristic Matching enables one to evolve
the whole space-time matching the boundaries of Cauchy and Characteristic
evolution. The methodology of Cauchy Characteristic Matching has been
successful in numerical evolution of the spherically symmetric
Klein-Gordon-Einstein field equations as well as for 3-D non-linear wave
equations. In this thesis the same methodology is studied in the context of the
Einstein equations.
