Gravity is one of the four fundamental interactions in physics. Einstein's General Theory of Relativity contains Newton's theory of gravity as a classical boundary case and describes gravity as the curvature of space-time. Experiments have confirmed the General Theory of Relativity with high accuracy, e.g. for the deflection of light rays and time measurements in GPS. It describes black holes, the Big Bang and gravitational waves.
In numerical relativity, Einstein's field equations are solved on the computer.
Numerical solving these 10 coupled, highly nonlinear partial differential equations allows the investigation of
Numerical relativity complements analytical methods and perturbation theory, and allows the calculation of phenomena that cannot be investigated by other methods.
Of particular interest is the calculation of gravitational waves. While the methods of perturbation theory provide the waveforms in the phase of the spiralling in of binary black holes, it is possible in numerical relativity theory to determine waveforms of the fusion phase. These simulated gravitational wave signals are helpful in the detection of gravitational waves.
Solving Einstein's field equations on the computer is a big challenge. It is necessary to cover many different topics.