Solutions of the Einstein field equations

rdf:langString Solutions of the Einstein field equations

rdf:langString Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact. The Einstein field equations are where is the Einstein tensor, is the cosmological constant (sometimes taken to be zero for simplicity), is the metric tensor, is a constant, and is the stress–energy tensor. The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime manifold. The Einstein tensor is built up from the metric tensor and its partial derivatives; thus, given the stress–energy tensor, the Einstein field equations are a system of ten partial differential equations in which the metric tensor can be solved for.