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A proposal of foundation of spacetime geometry

Research paper by Romualdo Tresguerres

Indexed on: 04 Aug '14Published on: 04 Aug '14Published in: General Relativity and Quantum Cosmology



Abstract

A common approach to metric-affine, local Poincar\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to alternative concepts of spacetime. In particular, the construction of the Minkowski metric, and its required invariance, allows either to reorganize the original affine bundle as a metric-affine geometry with explicit Lorentz symmetry, or to restrict it to a Poincar\'e geometry, both of them constituting the background of a wide class of gauge theories of gravity.