In this thesis, we will present some exact Finslerian solutions to a Finsler Einstein Equation. The first chapter contains an introduction to the main concepts of Finsler geometry. In particular,...Show moreIn this thesis, we will present some exact Finslerian solutions to a Finsler Einstein Equation. The first chapter contains an introduction to the main concepts of Finsler geometry. In particular, the mathematical concepts necessary to develop Finsler General Relativity will be introduced. We will briefly elaborate on properties of pp-waves in General Relativity, followed by a presentation of the main ideas of Very Special Relativity (VSR). VSR assumes a reduced symmetry of nature that is a subgroup of the full Lorentz group. A deformation of VSR symmetries gives rise to a Finsler treatment of spacetime, General Very Special Relativity (GVSR). We will extend GVSR in order to incorporate curved spacetimes. Then, we investigate whether the GVSR versions of VSI metrics (including pp-wave metrics) and AdS metrics in four and five dimensions are solutions to the Finsler Einstein equation proposed by Pfeifer. For the former, this is indeed the case (under certain conditions), but the latter raise the problem of a Finsler generalization of a cosmological constant, which we cannot resolve yet. Finally, we give an overview on experiments that have been proposed to detect (G)VSR deviations from Riemannianity and violations of Lorentz invariance. We conclude with a summary of our results and an outlook on further research.Show less
