Einstein-Cartan formulation of Chern-Simons Lorentz Violating Gravity

M. BOTTA CANTCHEFF

PHYSICAL REVIEW D - PARTICLE AND FILDS

APS

Año: 2008 vol. 78 p. 1 - 8

0556-2821

 We consider a modification of the standard Einstein theory in four dimensions, alternative to Ref. cite{JPI}, since it is based on the first order (Einstein-Cartan) approach to General Relativity, whose gauge structure is manifest. This is done by introducing an additional topological term in the action which becomes a Lorentz violating term by virtue of the dependence of the coupling on the space-time point. We obtain a condition on the solutions of the Einstein equations such that they persist in the deformed theory, and show that the solutions remmarkably correspond to the classical solutions of a collection of independent 2+1-d (topological) Chern-Simons gravities. Finally, we study the relation with the standard second order approach and argue that they both coincide to leading order in the modulus of the Lorentz violating vector field.