Singular Spacetimes
On Penrose’s analogy between spacetime curvature and optical lenses

In the lead-up to his singularity theorem, Roger Penrose was inspired by an analogy between Ricci Φ_00 scalar and Weyl Ψ_0 scalar dominated spacetime curvature and anastigmatic and astigmatic optical lenses respectively. This analogy allowed Penrose to relate total energy-momentum
flux across systems by the total focusing power of their optical counterpart. This, in turn, suggested a well defined energy of certain non-local Weyl curvature. The analogy between Weyl and astigmatic lenses was weakened in Lehmkuhl et al. (2024) to the two being only similar, but not identical. In this thesis we will argue that for a saddle lens, the analogy is perfect. We also provide an example where the relationship between total focusing power of a system and total energy-momentum flux seems to break down, as it allows for a gravitational wave with a negative localized energy.
Bachelor thesis in physics by Thijs Hogenkamp (2025)
Supervised by: Dr. Niels Martens (HPS), Sanne Vergouwen (HPS), Prof. Dr. Stefan Vandoren (Physics)
Second reader: Dr. Umut Gursoy (Physics)
Black Holes as Massive Spacetimes

What, if anything, makes the M in the Schwarzschild metric a physical mass? In this paper we present and evaluate various possible interpretations of M, all of which seem to capture some essential aspect of mass in the context of general relativity. We argue that the different interpretations give contradicting verdicts on whether supersubstantivalism is the appropriate ontology of static black holes described by the Schwarzschild solution to general relativity, suggesting that the spacetime-matter dichotomy is best given up. This conclusion is furthermore supported by a detailed conceptual analysis of two of the mass interpretations: the global ADM interpretation, and the special relativity trickle down interpretation.
Sanne Vergouwen & Niels Martens (in progress)