Singular Spacetimes
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)
The analysis of singular structure in the Kerr spacetime and physically more realistic spacetimes
In 1915, Karl Schwarzschild obtained his famous Schwarzschild solution, the first analytical solution to the vacuum Einstein Field Equations. This solution contained regions where the metric diverges, soon to be referred to as ‘metric singularities’. Ever since, the nature of spacetime singularities has been point of discussion among physicists and philosophers. The relevance of singular spacetime increased even more when Penrose published his fist singularity theorem, implying that singular structure is inevitably predicted by general relativity. This thesis provides an extensive analysis of the singular structure that arises in the Kerr spacetime and in physically more realistic spacetimes. For this purpose, the physical and mathematical nature of these types of singular structure is examined. Furthermore, by means of the ideas of Dennis Lehmkuhl, Erik Curiel and Karen Crowther & Sebastian De Haro, interpretations for singular spacetime structure will be analyzed. It will be stressed that some views on singular spacetime challenge our current singular black hole paradigm, while others embrace it. In addition, it will be examined to what extent Lehmkuhl’s historical interpretations for singular spacetime can be projected onto the Kerr solution. Finally, I will propose a classification to distinguish between possible approaches to constructing an adequate non-vacuum description for physically realistic gravitational collapse, based on a tension in different interpretations for singular structure.
by Sam Meijer (2025)
Supervised by: Dr. Niels Martens (HPS) & Sanne Vergouwen (HPS)
Third reader: Dr. Guido Bacciagaluppi (HPS)
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)
