Finsler Geometry, Spacetime Gravity – from Metrizability of Berwald Spaces to Exact Vacuum Solutions in Finsler Gravity

This PhD dissertation covers a range of topics in Finsler geometry andFinsler gravity, most notably: (i) the characterization of Berwald spaces, (ii)pseudo-Riemann (non-)metrizability of Berwald spaces, (iii)(α,β)-metrics, (iv) exact solutions to Pfeifer and Wohlfarth'svacuum field equation in Finsler gravity, and (v) Finsler gravitational wavesand their observational signature. An extended abstract can be found in thedissertation itself.