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Albert Einstein edited Field Equations.tex
almost 11 years ago
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\section{Field Equations}
This is a set of 10 equations (FE) which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell's equations, the FE are used to determine the spacetime geometry resulting from the presence of mass-energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress-energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the FE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the FE are the components of the metric tensor. The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation.
\cite{10.1002/andp.19163540702} This is a change
$$
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8 \pi G}{c^4}T_{\mu\nu}
$$