2002/11/30 by G. Allemandi, Gianluca Allemandi, M. Francaviglia +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Chern–Simons theory #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Gauge theory #Gravitation #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum electrodynamics #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/20/3/307
published as Class.Quant.Grav. 20 (2003) 483-506 · 30 pages, no figures. References added
arxiv created 2002/12/04 · openalex publication_date 2003/01/15 · openalex created_date 2016/06/24 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/06
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 AdS 3 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 black-hole mechanics for the BTZ solution is then proved and the transition between the variation of conserved quantities in Chern–Simons AdS 3 gravity theory and the variation of conserved quantities in general relativity is analysed in detail.