General covariance

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In theoretical physics, general covariance (also known as diffeomorphism covariance) is the invariance of physical laws under arbitrary coordinate transformations.

In the context of Einstein's general theory of relativity, a physical law expressed in a generally covariant fashion takes the same mathematical form in all coordinate systems, and is implemented by expressing the equations of physics in terms of tensor fields. All known fundamental physical theories, such as electrodynamics, have a generally covariant formulation.

Armed with general covariance Einstein was then able to extend the global Lorentz covariance in Special Relativity (which applies to all inertial frames) to a local Lorentz covariance in General Relativity (which applies to all frames, inertial and non-inertial). The Lorentzian metric can be locally reduced everywhere to the Minkowski metric under a coordinate transformation

The general principle of relativity, as used in GR, is that the laws of physics must make the same predictions in all reference frames. This is an extension of the special principle of relativity, which deals only with non-accelerating frames, and general covariance is a realization of it.

External links

[General covariance and the foundations of general relativity: eight decades of controversy], by J. D. Norton

Reference

See section 7.1.

General covariance

External links

Reference

See also