| Summary: | Einstein’s theory of relativity provides a unified description of gravity as a ge-
ometrical property of spacetime. However, Einstein’s equations in this theory are
hard to solve as there are essentially 10 highly coupled second order partial differen-
tial equations in 4 independent variables to solve. Most analytical solutions abuse
properties such as symmetry, perturbations or approximation methods to attain a
final solution. In this final year project, review some of the existing techniques used
to solve Einstein’s field equation, as well as attempt to solve some cases of Einstein’s
field equations through constructing a vacuum spacetime metric by generating man-
ifolds of revolution around a curve.
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