Post-Minkowskian Gravity: Dark Matter as a Relativistic Inertial Effect?

Abstract

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.

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

References in corpus (9)

• Dark Energy from structure: a status report
• An Atomic Gravitational Wave Interferometric Sensor (AGIS)
• General Relativistic Effects in Atom Interferometry
• The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
• Relativistic Quantum Mechanics and Relativistic Entanglement in the Rest-Frame Instant Form of Dynamics
• New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems
• The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: I) The Equations of Motion in Arbitrary Schwinger Time Gauges

Cited by in corpus (3)

• Dark matter effects in vacuum spacetime
• Distortions of Robertson-Walker metric in perturbative cosmology and interpretation as dark matter and cosmological constant
• Fake dark matter from retarded distortions