Penrose's singularity theorem in a Finsler spacetime

TL;DR

This paper extends Penrose's singularity theorem from Lorentzian to Finsler spacetimes by redefining causal concepts and analyzing their properties in the Finslerian context.

Contribution

It introduces a translation of key causal concepts and the singularity theorem into Finsler geometry, highlighting differences from Lorentzian spacetime.

Findings

Causal concepts are successfully extended to Finsler spacetimes.

Definitions of focal points and trapped surfaces are adapted for Finsler geometry.

The singularity theorem is reformulated in the Finslerian setting.

Abstract

We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting.