Raychaudhuri equation and singularity theorems in Finsler spacetimes

TL;DR

This paper extends key singularity theorems and causality results from Lorentzian geometry to Finsler spacetimes, broadening the understanding of spacetime structure in a more general geometric setting.

Contribution

It proves that major singularity and causality theorems in Lorentzian geometry also hold in Finsler spacetimes, including topological censorship and horizon properties.

Findings

Singularity theorems extend to Finsler spacetimes.

Causality theory results are valid in Finslerian context.

Properties of horizons and conformal structures are preserved in Finsler geometry.

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.