Lorentz gauge-invariant variables in torsion-based theories of gravity
Daniel Blixt, Rafael Ferraro, Alexey Golovnev, María-José Guzmán
Abstract
General relativity dynamics can be derived from different actions---which depart from the Einstein-Hilbert action in boundary terms---and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general relativity is a torsion-based theory for the tetrad field. More general torsion-based theories have been built in the last years, intending to supersede general relativity. There are two current ways to formulate such theories; one includes a spin connection and the other does not. We discuss the notion of Lorentz gauge invariance in such theories, and give a simple but important proof that both formulations are physically equivalent.
Topics & Concepts
General relativityLorentz covariancePhysicsTheoretical physicsAction (physics)Simple (philosophy)Theory of relativityGauge theoryLorentz transformationClassical mechanicsConnection (principal bundle)Spin connectionTetradBoundary (topology)Current (fluid)Four-forceTest theories of special relativityGauge (firearms)MathematicsGravitationMathematical physicsCovariant transformationSpin (aerodynamics)Rest (music)Boundary value problemPrinciple of relativityDifferential geometryIntroduction to gauge theoryOne-way speed of lightGeneral theoryInvariance principleNoncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesBlack Holes and Theoretical Physics