Giampiero Esposito, "What are the points at infinity?"

Wednesday 13 Mar 2024, 16:00 → 17:00 Europe/Rome

2G26

The concept of points at infinity comes into play when studying the action principle, or gravitational radiation or spacetime singularities in general relativity. First of all, how can we define such points in the first place? How to understand from first principles why a part of infinity consists of isolated points, whereas another part of infinity consists of a three-dimensional manifold? In this seminar the methods of projective geometry are applied in order to bring infinity down to a finite distance and hence answer the above questions. This geometric definition of infinity can be applied, for example, to spacetime models with spherical symmetry, and to the Godel universe. Interestingly, we can therefore define points at infinity even when the more familiar construction of conformal boundary does not exist. Thus, our framework might have a wide range of applications in theoretical physics.