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Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes , gravitational waves , neutron stars and many other phenomena described by Albert Einstein's theory of general 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 ...
Numerical solution for binary black hole (1960s–2005): The numerical solution of the two body problem in general relativity was achieved after four decades of research. Three groups devised the breakthrough techniques in 2005 (annus mirabilis of numerical relativity). [109]
If one is only interested in the weak field limit of the theory, the dynamics of matter can be computed using special relativity methods and/or Newtonian laws of gravity and the resulting stress–energy tensor can then be plugged into the Einstein field equations. But if one requires an exact solution or a solution describing strong fields ...
Numerical relativity is a (relatively) new field interested in finding numerical solutions to the field equations of both special relativity and general relativity. Computational particle physics deals with problems motivated by particle physics.
Relativity is a falsifiable theory: It makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation. [12]
In general relativity, four-dimensional vectors, or four-vectors, are required. These four dimensions are length, height, width and time. A "point" in this context would be an event, as it has both a location and a time. Similar to vectors, tensors in relativity require four dimensions. One example is the Riemann curvature tensor.
Despite the introduction of a number of alternative theories, general relativity continues to be the simplest theory consistent with experimental data. Reconciliation of general relativity with the laws of quantum physics remains a problem, however, as there is a lack of a self-consistent theory of quantum gravity.