Energy in General Relativity
The Status of the Classical Energy Conditions in General Relativity
For over half a century the classical energy conditions have been used as constraints on the Einstein Field Equations and have led to groundbreaking work in black hole physics and cosmology, among others. However, over time violations have been found, and the existence of classical violations that can be made arbitrarily large has led to discussion regarding their status within (and beyond) general relativity. In this thesis I look at the classical energy conditions in more detail, and determine that although complete abandonment is not necessary, the classical energy conditions can no longer be seen as fundamental parts of general relativity and their consequences should come with substantial asterisks.
Bachelor Thesis in Physics by Diederik Bots (2025)
Supervised by: Dr. Niels Martens (HPS) & Dr. Elisa Chisari (Physics)
Third reader: Prof. Dr. Stefan Vandoren (Physics)
Einstein on the Energy of Gravitational Waves
In 1916, Albert Einstein first predicted the existence of gravitational waves from his theory of general relativity. This paper contained a calculational mistake in the energy-momentum of the gravitational field and an unconvincing argument to discard gravitational wave solutions that do no carry energy, based on the idea that unimodular coordinate systems are a natural choice of coordinate systems. In 1918, Einstein published a second paper on gravitational waves, correcting the energy-momentum and showing that the energy-free waves are the result of a coordinate transformation. This thesis compares Einstein鈥檚 papers from 1916 and 1918, correcting his expression for the energy-momentum and comparing his arguments for discarding the gravitational wave solutions that do not carry any energy. Furthermore, the debate surrounding the non-tensorial nature of the gravitational energy-momentum is reviewed.
Bachelor Thesis in Physics by Fenna Roovers (2025)
Supervised by: Prof. Dr. Chris van den Broeck (Physics) & Dr. Niels Martens (HPS)
Third reader: Dr. Tanja Hinderer (Physics)
On Penrose鈥檚 analogy between spacetime curvature and optical lenses
In the lead-up to his singularity theorem, Roger Penrose was inspired by an analogy between Ricci 桅_00 scalar and Weyl 唯_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). An article based upon this thesis is in progress, co-authored with (Physics, 木瓜福利影视 of Bonn)
Supervised by: Dr. Niels Martens (HPS), Sanne Vergouwen (HPS), Prof. Dr. Stefan Vandoren (Physics)
Second reader: Dr. Umut Gursoy (Physics)