Local Lorentz covariance
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A local Lorentz covariance or local Lorentz symmetry is a local symmetry of space-time which reduces locally (i.e. as the region of space time under consideration shrinks) to a Lorentz symmetry. Any theory which exhibts a local lorentz symmetry is said to be locally Lorentzian.
General relativity is locally Lorenztian.
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