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The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
Massless particles have zero rest mass. The Planck–Einstein relation for the energy for photons is given by the equation E = hf, where h is the Planck constant and f is the photon frequency. This frequency and thus the relativistic energy are frame-dependent.
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
where is the Einstein tensor, is the cosmological constant (sometimes taken to be zero for simplicity), is the metric tensor, is a constant, and is the stress–energy tensor. The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime ...
Einstein also examined relativistic aberration and the transverse Doppler effect. [4] The fourth, a consequence of special relativity, developed the principle of mass–energy equivalence, expressed in the equation = and which led to the discovery and use of nuclear power decades later.
In general relativity, the stress–energy tensor is studied in the context of the Einstein field equations which are often written as + =, where = is the Einstein tensor, is the Ricci tensor, = is the scalar curvature, is the metric tensor, Λ is the cosmological constant (negligible at the scale of a galaxy or smaller), and = / is the ...
The Einstein field equations (EFE) are the core of general relativity theory. The EFE describe how mass and energy (as represented in the stress–energy tensor) are related to the curvature of space-time (as represented in the Einstein tensor).
The equation is often written this way because the difference is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where m > 0 and p = 0, this equation again expresses the mass–energy equivalence E = m.