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Numerical relativity is a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativity. Despite promising results, accurate and validated algorithms for Einstein's equations remain elusive. The size and complexity of the equations along with persisting inquiries in fundamental issues of relativity theory are attributed the cause of thus far unsuccessful attempts at resolution. Nonetheless, the field has prodigiously expanded in recent years as engaging research continues.

Numerical relativity aims for comprehensive understanding of the complex nature of strong dynamical gravitational fields. Another topic under investigation in numerical relativity is the initial value problem of vacuum relativity. This involves partial differential equations, discretization techniques for these equations, treatment of black hole spacetimes, and the imposition of boundary conditions.

Numerical relativity research is distinct from work on classical field theories as many techniques implemented in these areas are inapplicable in relativity. Many facets are however shared with large scale problems in other computational sciences like computational fluid dynamics, electromagnetics, and solid mechanics. Numerical relativists often work with applied mathematicians and draw insight from numerical analysis, scientific computation, partial differential equations, and geometry among other mathematical areas of specialization.

Einstein field equation

The field equation reads, in components, as follows:

${\displaystyle R_{ab}-{R \over 2}g_{ab}+\Lambda g_{ab}={8\pi G \over c^{4}}T_{ab}}$

where ${\displaystyle R_{ab}}$ are the Ricci curvature tensor components, ${\displaystyle R}$ is the scalar curvature, ${\displaystyle g_{ab}}$ are the metric tensor components, ${\displaystyle \Lambda }$ is the cosmological constant, ${\displaystyle T_{ab}}$ are the stress-energy tensor components describing the non-gravitational matter, energy and forces at any given point in space-time, ${\displaystyle \pi }$ is pi, ${\displaystyle c}$ is the speed of light in a vacuum and ${\displaystyle G}$ is the gravitational constant which also occurs in Newton's law of gravity.

See also

• Mathematics of general relativity

Links

http://www.emis.ams.org/journals/LRG/Articles/lrr-2003-3/node19.html

• Relativity
• Computational physics