In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical laws under arbitrary differentiable coordinate transformations.
While this concept is exhibited by general relativity, which describes the dynamics of spacetime, one should not expect it to hold in less fundamental theories.
[2] Einstein recognized that the general principle of relativity should also apply to accelerated relative motions, and he used the newly developed tool of tensor calculus to extend the special theory's global Lorentz covariance (applying only to inertial frames) to the more general local Lorentz covariance (which applies to all frames), eventually producing his general theory of relativity.
Much of the work on classical unified field theories consisted of attempts to further extend the general theory of relativity to interpret additional physical phenomena, particularly electromagnetism, within the framework of general covariance, and more specifically as purely geometric objects in the spacetime continuum.
The relationship between general covariance and general relativity may be summarized by quoting a standard textbook:[3] Mathematics was not sufficiently refined in 1917 to cleave apart the demands for "no prior geometry" and for a geometric, coordinate-independent formulation of physics.