General Relativity and Weyl Geometry:. Towards a New Invariance Principle
Abstract
Our aim in this talk is to show that one can formulate general relativity using the language of a non-Riemannian geometry, namely, the one known as Weyl integrable geometry. In this formulation, general relativity appears as a theory in which the gravitational field is described simultaneously by two geometrical fields: the metric tensor and the Weyl scalar field, the latter being an essential part of the geometry, manifesting its presence in almost all geometrical phenomena, such as curvature, geodesic motion, and so on. In this new geometrical setting, general relativity exhibits a new kind of invariance, namely, the invariance under Weyl transformations. We are then led to a scenario in which the gravitational field is not associated only with the metric tensor, but with the combination of both the metric and the geometrical scalar field
- Publication:
-
Particle Physics at the Tercentenary of Mikhail Lomonosov - Proceeding of the Fifteenth Lomonosov Conference on Elementary Particle Physics. Edited by Studenikin Alexander I.. Published by World Scientific Publishing Co. Pte. Ltd
- Pub Date:
- November 2013
- DOI:
- 10.1142/9789814436830_0088
- Bibcode:
- 2013pptm.conf..408R