Randers pp-waves

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.

arXiv comment11 pagers, updated to journal version

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Cited by in corpus (10)

• Mathematical foundations for field theories on Finsler spacetimes
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• A Cosmological Unicorn Solution to Finsler Gravity
• Relativistic deformed kinematics: from flat to curved spacetimes
• The Finsler spacetime condition for (α,β)-metrics and their isometries
• Cosmological Landsberg Finsler spacetimes
• More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques