2006/04/27 by Luca Lusanna
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical mechanics #Cosmology and Gravitation Theories #Equivalence principle (geometric) #General relativity #Gravitation #Gravitational field #Inertial frame of reference #Mathematical physics #Mathematics #Minkowski space #Physics #Relativity and Gravitational Theory #Theoretical physics #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1142/s0219887807001874
published as ECONFC0602061:05,2006; Int.J.Geom.Meth.Mod.Phys.4:79-114,2007 · 33 pages, Lectures given at the 42nd Karpacz Winter School of Theoretical Physics, "Current Mathematical Topics in Gravitation and Cosmology", Ladek, Poland, 6-11 February 2006
arxiv created 2006/04/27 · openalex publication_date 2007/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3 + 1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deparametrization to special relativity and the subsequent possibility to take the non-relativistic limit.