Structural theory of Lorentzian length spaces

There is a new approach to General Relativity, Einsteins theory of gravity called Lorentzian length spaces, built in the spirit of metric geometry. In this project, Tobias Beran has the goal to better describe such generalized spaces where there is a bound on how attractive or repulsive the tidal forces of gravity can be. These forces have the effect of the tides on earth and in extreme cases spagghetification when falling into a black hole. These bounds can be described by comparing triangles to triangles in a model space: one can see positive curvature on the surface of a sphere by triangles having a larger-than-normal angle sum, e.g. there are triangles with three right angles. This project on the one hand wants to give different descriptions of such spaces which are technically useful. Also, I want to show that in spaces with a bound on the repulsive tidal forces when only measuring them in small patches also large-scale objects cannot feel excessive tidal forces. On the other hand, the main part of the project is describing spaces with a bound on the attractive tidal forces cannot be very wild: the space can only have features similar to that of a cube: there will be faces where the space is quite tame, edges where the space is only tame in one direction and corners which represent the more severe singularities.