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Extended solution space for Chern-Simons gravity

Extended solution space for Chern-Simons gravity

A new “twist” to GR

A new “twist” to GR extended by CS a term• So far the symmetric (torsion free) connection is a choice.• Is it the cause of the restricted space of solutions?• Little room for finding new solutions of EH + CS. Basically the model is probed by seeingwhich solutions to GR have a P = 0.• We propose to study a similar theory by relaxing thetorsion-free condition.. . . To be determined dynamically.S T [g] → S T [e c ,ω a b].VIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 9

A new “twist” to GR + CS, contd• Non-symmetric connecction → ω c b. Torsion ≠ 0 without fermions, however!!!Tetrad formalism more amenable for studying local Lorentz symmetry.• Dynamical variables: tetrad e b and connection ω c bone-forms. The action readsS[e c ,ω a b] = κ ∫ ()R ab ∧ ∗ (e a ∧ e b ) + βϑ R a b ∧ R b a ,2where the Riemann R ab and torsion T a two-forms are defined as usualR a b = dω a b + ω a c ∧ ω c b , T a = de a + ω a b ∧ e b .• As in the JP formulation ϑ, is non-dynamical.• β as a small dimensionless parameter, which serves as a bookkeeping device.VIII Silafae - UTFSM, Valparaíso, 2010 Mauro Cambiaso New solutions in Chern-Simons gravity – p. 10

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