Vectors can equal another vector plus a scalar term {gauge, relativity}|. Scalar gauges can change with position. For example, space-time curvature can change with position, and gauges can represent linear curvature changes with position.
Using linear transformations {gauge transformation}, gauges can relate vectors expressed in different coordinate systems. Gravitation, electromagnetism, and chromodynamics use gauge transformations to model infinitesimal, finite, scalar-coordinate transformations. For local space-time regions, general relativity is invariant under finite coordinate transformations, and a generalized gauge transformation represents general relativity. Using gauge scalars can simplify differential equations.
Because derivatives of scalars equal zero, gauge changes do not affect physical measurements, motion differential equations do not change, and gauge transformations preserve invariants.
In gravitational fields so weak that space-time has negligible curvature, gravity does not move gravitational-field-source masses and does no work on them, so masses have no self-energy. For this case, theories {linearized theory of gravity} represent space-time-coordinate changes as infinitesimal gauge changes, which change space-time-metric coefficients.
5-Physics-Relativity-General Relativity-Theory
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Date Modified: 2022.0225