Causal structure and electrodynamics on Finsler spacetimes

Christian Pfeifer and Mattias N. R. Wohlfarth
Phys. Rev. D 84, 044039 – Published 12 August 2011

Abstract

We present a concise new definition of Finsler spacetimes that generalizes Lorentzian metric manifolds and provides consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces, we show that geometric objects like the Cartan nonlinear connection and its curvature are well defined almost everywhere on Finsler spacetimes, including their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with a null boundary, as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.

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  • Received 7 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.044039

© 2011 American Physical Society

Authors & Affiliations

Christian Pfeifer* and Mattias N. R. Wohlfarth

  • II. Institut für Theoretische Physik und Zentrum für Mathematische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

  • *christian.pfeifer@desy.de
  • mattias.wohlfarth@desy.de

See Also

Finsler geometric extension of Einstein gravity

Christian Pfeifer and Mattias N. R. Wohlfarth
Phys. Rev. D 85, 064009 (2012)

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Vol. 84, Iss. 4 — 15 August 2011

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