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The Einstein field equations (EFE) or Einstein's equations are a set of ten equations in Einstein's theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.[1] They were first published in 1915.[2]. The EFE collectively form a tensor equation and equate the curvature of spacetime (as expressed using the Einstein tensor) with the energy and momentum within the spacetime (as expressed using the stress-energy tensor). The EFE are used to determine the curvature of spacetime resulting from the presence of mass and energy. That is, they determine the metric tensor of spacetime for a given arrangement of stress-energy in the spacetime. Because of the relationship between the metric tensor and the Einstein tensor, the EFE become a set of coupled, non-linear differential equations when used in this way. The Einstein field equations (EFE) may be written in the form[1]
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