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The electromagnetic stress–energy tensor in the International System of Quantities (ISQ), which underlies the SI, is [1] = [], where is the electromagnetic tensor and where is the Minkowski metric tensor of metric signature (− + + +) and the Einstein summation convention over repeated indices is used.
In the relativistic formulation of electromagnetism, the nine components of the Maxwell stress tensor appear, negated, as components of the electromagnetic stress–energy tensor, which is the electromagnetic component of the total stress–energy tensor. The latter describes the density and flux of energy and momentum in spacetime.
The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,
The electromagnetic stress–energy tensor can be interpreted as the flux density of the momentum four-vector, and is a contravariant symmetric tensor that is the contribution of the electromagnetic fields to the overall stress–energy tensor: = (/ + / / / / / / /), where is the electric permittivity of vacuum, μ 0 is the magnetic ...
Another covariant electromagnetic object is the electromagnetic stress-energy tensor, a covariant rank-2 tensor which includes the Poynting vector, Maxwell stress tensor, and electromagnetic energy density.
is the Einstein tensor, G is the Newtonian constant of gravitation, g ab is the metric tensor, and R (scalar curvature) is the trace of the Ricci curvature tensor. The stress–energy tensor is composed of the stress–energy from particles, but also stress–energy from the electromagnetic field. This generates the nonlinearity.
In the tensor calculus formulation, the electromagnetic tensor F αβ is an antisymmetric covariant order 2 tensor; the four-potential, A α, is a covariant vector; the current, J α, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂ α is the partial derivative with respect to the coordinate, x α.
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.