Randers pp-waves

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 turns out to be composed of a Ricci-flat, CCNV (covariantly constant null vector) Lorentzian spacetime, or Brinkmann space, and a 1-form defined by its CCNV. Since the pp-waves are the most well-known metric in this class, we refer to the found solutions as Randers pp-waves.

Automated summary

In this work, Randers spacetimes of Berwald type in Finsler gravity were studied, showing that the field equation for this class is equivalent to the vanishing of the Finsler Ricci tensor, similar to Einstein gravity. Exact solutions for vacuum Finsler gravity in the form of Ricci-flat Lorentzian spacetime and a 1-form defined by CCNV were constructed, with these solutions referred to as Randers pp-waves due to their association with the well-known pp-waves in this class.