The Schwarzschild spacetime and cosmological constant, by constructing manifolds of revolution

Abstract

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.