Gravity in three plus epsilon dimensions

Einsteins general relativity is our best theory of gravity. Yet many of its most intriguing predictions, such as black hole formation from the collapse of matter and the nature of spacetime near singularities, are notoriously difficult to analyze, and its quantum version remains elusive. To gain conceptual insights, we often employ simpler models of gravity in lower dimensions: instead of four spacetime dimensions, one can consider only three or two. But this simplicity comes at a cost. In two dimensions, Einstein gravity ceases to exist. In three dimensions (3D), a long-range Newtonian force is absent in Einstein gravity (unlike in Newtons theory), and black holes can only exist if a negative cosmological constant is present (unlike in our Universe). This project introduces a novel approach that can overcome all these difficulties: studying gravity in three plus epsilon dimensions, where spacetime has just slightly more than three dimensions. The primary goal is to develop and study a new, Einstein-like theory of gravity in D = 3 + e dimensions, which recovers expected physical behavior like Newtonian long-range forces and admits black hole solutions even without a cosmological constant. Our approach also allows the simulation of black hole formation from matter collapse and the investigation of universal "critical phenomena," offering parallels to phase transitions in condensed matter physics. A particular focus is the numerical construction of spacetime crystals, which we intend to do using the resources of the Vienna Scientific Cluster. These spacetime crystals are exotic geometries that are neither black holes nor vacuum, but sit precisely at the threshold of black hole formation. These structures determine the observables of critical gravitational collapse. The parameter e plays another important technical role: it behaves like a small coupling constant in quantum field theory, enabling perturbative techniques. This complements existing studies in the opposite limit (D 8), where gravity becomes strongly coupled. Led by theoretical physicist Daniel Grumiller (TU Wien) and involving early-career researchers and key collaborators across Europe, this project lies at the intersection of classical gravity, numerical relativity, quantum gravity, and holography. It seeks not only to advance our fundamental understanding of black holes and gravity but also to train the next generation of researchers working at the frontier of theoretical physics.