Observer dependent geometries

Abstract

From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.

43 pages, 2 figures; invited contribution to "Mathematical Structures of the Universe", Copernicus Center Press, Krakow, 2014, ISBN 978-83-7886-107-2; minor corrections to match published version

References in corpus (2)

• Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity

Cited by in corpus (2)

• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Kinetic gases in static spherically symmetric modified dispersion relations