Carrollian gravity and black holes

Carrollian gravity was named in honor of Lewis Carroll`s "Through the Looking-Glass": there is a scene where Alice encounters the Red Queen, who says "Now, here, you see, it takes all the running you can do, to keep in the same place." In Carrollian physics, the speed of light approaches zero. This limit is opposite from the everyday situation, where the speed of light tends to infinity, for most practical purposes. Carrollian symmetries were first described in seminal work by Levy-Leblond in 1965 but had not attracted much attention until recently when Carrollian structures emerged in various situations - for instance, when approaching a black hole or in condensed matter systems with limited mobility (where so-called "fractons" arise). Carrollian gravity follows the logic of Einstein that led from special to general relativity. However, Carrollian gravity still lies in its infancy. In particular, it is unknown whether such theories are compatible with one of the most striking predictions of general relativity, black holes. Currently, we have two conflicting expectations. On the one hand, the traditional black hole definition requires the existence of a "lightcone", which is only possible for a finite speed of light. This notion, therefore, cannot exist in Carrollian gravity. On the other hand, we have recently constructed exact solutions of Carrollian gravity that seem to have analogous properties to usual black holes: mass, temperature, entropy, and a first law of "black hole mechanics" connecting these three observables. Moreover, there are indications from toy models in two dimensions that the holographic principle works for Carrollian gravity - i.e., there is a dual formulation of the theory without gravity and in one lower dimension. The main goal of this FWF project is to define a meaningful geometric notion of black holes in Carrollian theories of gravity and to study the consistency and applications of this notion, including holographic aspects. The crucial technical concept that we intend to develop and explore is a Carrollian extremal surface. Such a surface remains invariant under Carrollian boosts. A similar surface (called bifurcation surface) exists for black holes in general relativity and could be a pivotal geometric property for defining Carrollian black holes. This FWF project will hire a postdoc, selected internationally through the Leuven network for postdocs in theoretical high energy physics and a Ph.D. student. It also involves international collaborators from Europe, UK, India, and Brazil.