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The metric (=field of metric tensors) is the solution of Einstein's field equations when a special distribution of matter is given. It is among the unsolved problems of physics to calculate the metric …

Is the equation $g_{\mu\nu} =$ diag (-1,1,1,1)$\cdot$ const. + $T_{\mu\nu}$ equivalent to Einstein's field equations? $g_{\mu\nu}$ is the metric tensor and describes the curvature and $T_{\mu\nu}$ de …

In relativity theory, the metric tensor $$g_{\mu\nu} $$ describes the gravitational field. Can one treat the determinant of the metric tensor, normalized by the square of the Jacobian of the transform …

Let's have a look at the Schwarzschild solution. Let's consider only the spatial part since my question is only regarding length contraction. There is the coefficient of the radial component, it's $\f …

I'm trying to understand the derivation of the Schwarzschild metric from Wikipedia, but I simply do not understand why, therein, $g_{22}$ and $g_{33}$ must be those of the flat spacetime. Couldn't $g_ …

A field of metric tensors fully characterises the curvature of a vacuum space-time. (For example, the spacetime between some single point masses which are themself not part of the manifold) The metric …

Curvature of space-time (in General Relativity) is described using the metric tensor. The metric tensor, however, relies on the choice of coordinates, which is totally arbitrary. See for example answe …

$g_{\mu\nu}$ is the metric tensor. It describes the curvature of spacetime in general relativity. The choice of coordinates is completely arbitrary. It should be possible to find and chose coordinates …