Lorentz Violation and Gravity

Lorentz symmetry lies at the heart of relativity and is a feature of low-energy descriptions of nature. Minuscule Lorentz-violating effects arising in theories of quantum gravity offer a promising candidate signal for new physics at the Planck scale. A framework is presented for incorporating Lorentz violation into general relativity and other theories of gravity. Applying this framework yields a proof that explicit Lorentz symmetry breaking is incompatible with generic Riemann-Cartan geometries. The framework also enables the construction of all possible terms in the effective low-energy action for the underlying quantum gravity. These terms form the gravitationally coupled Standard-Model Extension (SME), which offers a comprehensive guide to searches for observable phenomena. The dominant and subdominant Lorentz-violating terms in the gravitational and QED sectors of the SME are discussed.