In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures...

differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...

tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general relativity...

obtained from the Riemann tensor by subtracting a tensor that is a linear expression in the Ricci tensor. In general relativity, the Weyl curvature is the...

a metric space A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold Metric tensor (general...

stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...

quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear...

coordinates Diffusion tensors, the basis of diffusion tensor imaging, represent rates of diffusion in biologic environments In general relativity, four-dimensional...

In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface)...

It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of Riemannian metrics that measures...

Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric. The vanishing of the Cotton tensor for...

relativity is being squashed to zero. The same is true of vector–tensor theories, the deviation of the vector–tensor theories from general relativity...

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field...

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation...

manifold) or of the physical space. Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and...

called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian...

the Einstein tensor, g μ ν {\displaystyle g_{\mu \nu }} is the metric tensor, T μ ν {\displaystyle T_{\mu \nu }} is the stress–energy tensor, Λ {\displaystyle...

In mathematics, the signature (v, p, r)[clarification needed] of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric...

that the general principle of relativity should also apply to accelerated relative motions, and he used the newly developed tool of tensor calculus to...

mathematics, the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It is therefore a tensor field of order three....

with a metric tensor, g a b {\displaystyle g_{ab}} , and the gravitational field is represented (in whole or in part) by the Riemann curvature tensor R a...

Einstein tensor, computed uniquely from the metric tensor which is part of the definition of a Lorentzian manifold. Since giving the Einstein tensor does...

special relativity and general relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. General four-tensors are usually...

Einstein tensor (which is constructed from the metric) gμν is the inverse of the metric tensor, gμν g = det(gμν) is the determinant of the metric tensor. g...

differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing...

metric (FLRW), where it corresponds to an increase in the scale of the spatial part of the universe's spacetime metric tensor (which governs...

O(3, 1) for general relativity). Christoffel symbols are used for performing practical calculations. For example, the Riemann curvature tensor can be expressed...

notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern...

to the theory of relativity Problems with Einstein's general theory of relativity Ricci calculus – Tensor index notation for tensor-based calculations...

In general relativity, curvature invariants are a set of scalars formed from the Riemann, Weyl and Ricci tensors — which represent curvature, hence the...