Thursday 4 June 2026, 16:00 - 17:00 in HG00.086
Sjors Heefer (Eindhoven)
Finsler Gravity and Einstein Spacetimes
Finsler gravity is the extension of general relativity obtained by enlarging the class of allowed spacetime geometries from pseudo-Riemannian manifolds to Finsler manifolds of Lorentzian signature. The notion of an Einstein metric generalizes directly to the Finsler setting as well. In contrast to the pseudo-Riemannian case, however, not that much is known about these Einstein-Finsler metrics or their relation to solutions of the gravitational field equations; and only few explicit examples are known. In this talk, after introducing the fundamental notions in Finsler geometry and gravity, we focus on a particular class of Finsler metrics, the so-called `Kropina metrics'. First, we give necessary and sufficient conditions for such metrics to be of Einstein type, extending Zhang and Shen's characterization to all signatures. As a result, we are able to construct new explicit examples of Lorentzian Einstein-Finsler metrics. Second, we discuss the role of such metrics in Finsler gravity. In particular, we classify all solutions of Einstein-Kropina type to the Finsler gravitational field equation in vacuum with cosmological constant.