Diederik Bots

Diederik's bachelor thesis concerns negative lenses, negative energy & spacetime curvature. In the lead-up to Penrose's 1965 singularity theorem, he was inspired by an analogy between positive optical lenses (astigmatic and anastigmatic) and gravitational curvature (Ricci and Weyl), which allowed him to equate gravitational energy to focusing power in certain specific cases (Lehmkuhl et al., 2023; bachelor thesis Thijs Hogenkamp 2025). An obvious but unexplored extension of this analogy is between negative lenses and diverging geodesics, e.g. due to a cosmological constant or another form of dark energy. While negative lenses are unproblematic, most spacetime curvatures with negative energy (in the sense of violating specific classical energy conditions) tend to be considered problematic. In fact, most theorems in general relativity stand or fall with assuming one energy condition or another (Curiel, 2017), e.g. the positive energy theorem. Arguments/motivations are not always given; sometimes instability arguments are hinted at but it is not motivated that a problematic instability will universally occur when any of the energy conditions is violated. This project systematically analyses motivations for the four main classical energy conditions, starting with Bondi's 1957 paper on negative mass in GR, and Penrose's 1993 paper against negative mass in GR.