Program within Applied Differential Geometry

Spacetime geometry

Pushing the boundaries of Einstein’s relativity theory.

This `classical’ theory is written in the language of pseudo-Riemannian geometry. In spite of its tremendous success, it fails to explain striking phenomena at galactic and cosmological scales, and cannot be reconciled with quantum theory. This programme, supported by a personal grant from NWO (ENW domain, Physics discipline, formerly known as FOM), seeks remedies within the more powerful framework of pseudo-Finsler geometry.

Details: In order to accommodate unexplained spacetime and gravitational phenomena observed at galactic and cosmological scales, we need to extend our purview of Einstein’s relativity theory beyond its classical reach. Finsler geometry is a canonical extension of Riemannian geometry, aptly paraphrased as ‘Riemannian geometry without the quadratic restriction’. Since the classical theory is formulated in the language of (pseudo-)Riemannian geometry, a promising avenue is to view it as some (as yet poorly understood) limiting case of a more comprehensive (pseudo-)Finslerian framework. But, without any guiding principles, the latter brings in infinitely many new degrees of freedom, begging the question of how to apply Ockham’s razor in order to ‘make things as simple as possible, but not simpler’ in the light of new physical phenomena to be accounted for. Our approach to figure this out is to venture upon a heuristic program with a modest amount of foresight, stipulating a priori geometric constraints, and then investigating the pros and cons implied by these. Intriguing results have been obtained.