Black Holes
Black Holes as Massive Spacetimes
What, if anything, makes the M parameter in the Schwarzschild metric a physical mass? In this paper we present and evaluate five possible interpretations of the mass of a Schwarzschild black hole. We argue that the concept of black hole mass is best understood by taking each of these five interpretations into account. We particularly show how a global interpretation of mass succeeds in referring to black hole mass, in spite of its significant difference from the traditional Newtonian notion of mass that is local. Finally, we argue not only a) that this global interpretation shows that the spacetime–matter dichotomy breaks down at the intensional level—in the sense that these conceptual categories become mixed—but also b) that the various interpretations suggest that the spacetime–matter dichotomy is best given up altogether, at least in the Schwarzschild context.
Sanne Vergouwen & Niels Martens (under review)
The Birth of Gravitational Particle Creation: the Enduring Legacy of Leonard Parker's 1966 Thesis
This paper offers a historical overview of the origins and enduring significance of gravitational particle creation, a groundbreaking discovery first formulated in Leonard Parker's 1966 doctoral thesis at Harvard University. By tracing the context in which Parker developed this idea and examining its subsequent influence, the paper highlights how the concept of gravitational particle creation advanced the study of quantum field theory in curved spacetime and profoundly shaped modern cosmology, as well as the quantum theory of black holes.
Antonio Ferreiro, Jose Navarro-Salas, Silvia Pla (forthcoming)
Black Hole Thermodynamics and its Implications for the Spacetime-Matter Distinction
In this thesis, I study the implications of Black Hole Thermodynamics (BHT), in particular the second law of BHT, for the spacetime-matter dichotomy, which strictly distinguishes between spacetime and matter such that something is either spacetime or matter, never both, never neither. For the second law of BHT, I discuss three derivations: a quantum/statistical-mechanical derivation, a differential geometry derivation and a quasi-local method by metric perturbations. All three derive the same law but the differential geometry derivation, which is Hawking’s original derivation, is the most general derivation. The differential geometry derivation is indeed geometrical in essence, but also requires the Null Energy Condition (NEC). The NEC has logically equivalent (geometric and physical) formulations, but only a clear geometric interpretation. The other two derivations introduce more matter and energetic properties to the picture through their reliance on, for instance, Hamiltonians and the ADM mass. Viewing the three derivations together, there is no clear spacetime-matter distinction in the second law of BHT, since they show two sides of the same coin; spacetime and matter properties both describe the behavior of the black hole in the same way using different methods or even a mixture of properties. And also considering a wider picture of BHT, I argue that BHT blurs the spacetime-matter dichotomy.
Bachelor thesis in physics by Luc van den Bos (2026)
Supervised by: Dr. Niels Martens (HPS) & Prof. Dr. Stefan Vandoren (Physics)
Third reader: Prof. Dr. Chris van den Broeck
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.
Research Internship Thesis 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)
Fourth reader: Dr. Umut Gursoy (Physics)
