Raychaudhuri equation and singularity theorems in Finsler spacetimes

Abstract

The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler, or Kriele, but also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.

29 pages. v2: expanded treatment of conformal transformations; corrected an error on the conformal transformation of the Ricci scalar

References in corpus (9)

• Singularity Theorems and Their Consequences
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Light cones in Finsler spacetime
• Limit curve theorems in Lorentzian geometry
• Birefringence in pseudo-Finsler spacetimes
• Chronological spacetimes without lightlike lines are stably causal
• The connections of pseudo-Finsler spaces
• Non-imprisonment conditions on spacetime

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• Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Charged anisotropic strange stars in Finslerian geometry
• Affine sphere spacetimes which satisfy the relativity principle
• Differential Geometric Aspects of Causal Structures
• Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
• Pseudo-Finsler spaces modeled on a pseudo-Minkowski space
• Covariant kinematics of light in media and a generalized Raychaudhuri equation
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