are taken as the basic variables. A discrete version of the Einstein–Hilbert action is obtained by considering so-called deficit angles of these blocks, a zero deficit angle corresponding to no curvature. This novel idea finds application in approximation methods in numerical relativity and quantum gravity, the latter using a generalisation of Regge calculus. Singularity theorems In general relativity, it was noted that, under fairly generic conditions, gravitational collapse will inevitably result in a so-called singularity. A singularity is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges. Numerical relativity Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise. Novel techniques developed by numerical relativity include the excision method and the puncture method for dealing with the singularities arising in black hole spacetimes. Common research topics include black holes and neutron stars. Perturbation methods The nonlinearity of the Einstein field equations often leads one to consider approximation methods in solving them. For example, an important approach is to linearise the field equations. Techniques from perturbation theory find ample application in such areas. See also Notes [1] The defining feature (central physical idea) of general relativity is that matter and energy cause the surrounding spacetime geometry to be curved. References