Covariant charges in Chern-Simons AdS3 gravity

We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern-Simons theory, with particular reference to Chern-Simons AdS3 gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern-Simons Lagrangian and using a recipe developed by Allemandi et al (2002 Class. Quantum Grav. 19 2633-55, 237-58) to calculate the variation of conserved quantities. The problem of giving a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of blackhole mechanics for the BTZ solution is then proved and the transition between the variation of conserved quantities in Chern-Simons AdS3 gravity theory and the variation of conserved quantities in general relativity is analysed in detail.