Randers pp-waves

TL;DR

This paper investigates Randers spacetimes of Berwald type in Finsler gravity, showing their vacuum solutions correspond to Randers pp-waves, which are constructed from Lorentzian pp-wave spacetimes and null 1-forms.

Contribution

It provides a complete classification of vacuum solutions of Berwald-Randers type in Finsler gravity, linking them to Lorentzian pp-waves and establishing their equivalence with Rutz's equation.

Findings

Vacuum field equations reduce to vanishing Finsler Ricci tensor.

All exact solutions are Randers pp-waves composed of Lorentzian pp-waves and null 1-forms.

Randers pp-waves are characterized by covariantly constant null vectors.

Abstract

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer and Wohlfarth's vacuum field equation of Finsler gravity for this class. We show that in this case the field equation is equivalent to the vanishing of the Finsler Ricci tensor, analogously to Einstein gravity. This implies that the considered vacuum field equation and Rutz's equation coincide in this scenario. We also construct all exact solutions of Berwald-Randers type to vacuum Finsler gravity, which turn out to be composed of a CCNV (covariantly constant null vector) Lorentzian spacetime, commonly known as pp-wave, and a 1-form given by the pp-wave distinguished null vector. We therefore refer to the found solutions as Randers pp-waves.