2009/12/15 by Luca Lusanna · 3 citations
Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Equivalence principle (geometric) #General relativity #Gravitation #Inertial frame of reference #Mathematical physics #Minkowski space #Physics #Radioactive Decay and Measurement Techniques #Relativity and Gravitational Theory #astro-ph.GA #gr-qc #hep-th
paper · pdf · doi:10.1088/1742-6596/222/1/012016
published in Journal of Physics Conference Series 222, 012016 (IOP Publishing) · 15 pages. Talk at the {\it 1st Mediterranean Conference in Classical and Quantum Gravity}, held in the Orthodox Academy of Crete in Kolymbari (Greece) from Monday, September 14th to Friday, September 18th, 2009
arxiv created 2009/12/15 · openalex publication_date 2010/04/01 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Talk at the 1st Mediterranean Conference in Classical and Quantum Gravity , held in the Orthodox Academy of Crete in Kolymbari (Greece) from Monday, September 14th to Friday, September 18th, 2009. A review is given of the theory of non-inertial frames (with the associated inertial effects and the study of the non-relativistic limit) in Minkowski space-time, of parametrized Minkowski theories and of the rest-frame instant form of dynamics for isolated systems admitting a Lagrangian description. The relevance and gauge equivalence of the clock synchronization conventions for the identification of the instantaneous 3-spaces (Euclidean only in inertial frames) are described. Then this formalism is applied to tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times without super-translations, where the equivalence principle implies the absence of global inertial frames. The recently discovered York canonical basis, diagonalizing the York-Lichnerowicz approach, allows to identify the gauge variables (inertial effects in general relativity) and the tidal ones (the gravitational waves of the linearized theory) and to clarify the meaning of the Hamilton equations. The role of the gauge variable 3 K , the trace of the extrinsic curvature of the non-Euclidean 3-space (the York time not existing in Newton theory), as a source of inertial effects is emphasized. After the presentation of preliminary results on the linearization of tetrad gravity in the family of non-harmonic 3-orthogonal gauges with a free value of 3 K , we define post-Minkowskian gravitational waves (without post-Newtonian approximations on the matter sources) propagating in a non-Euclidean 3-space, emphasizing the non-graviton-like aspects of gravity. It is conjectured that dark matter may be explained as a relativistic inertial effect induced by 3 K : it would simulate the need to choose a privileged gauge connected with the observational conventions for the description of matter.