This course offers an advanced study of the curved space-time of general relativity. We will see how, under very general condition, such a space-time necessarily has singularities.
This means that black holes and the Big-Bang are not pathologies of general relativity, but are intrinsic to the theory.
The purpose of this course is to show Hawking's and Penrose's singularity theorems in general relativity (for which Penrose won the Nobel Prize in Physics in 2020). To get there, we will first study the notion of completeness and extensibility for pseudo-Riemannian varieties, then the cuasale struttsara of this variety. A key notion will be that of globally hyperbolic space, the starting point of numerous advanced arguments in general relativity.
Ability to confront well known mathematical concepts (completeness, metric space) in a new context (lorentzian geometry).
Knowledge of the mathematical tools required to study the causal structure of spacetime (global iperbolicity).
Developing a multidisciplinary scientific culture, at the cutting edge of recent advances in the field (study of black holes is currenbtly under a revolution, due to the discovery of black holes and the photographies of Event Horizon Telesecope).
Previous course of differential geometry and/or general relativity.
traditional
O'Neill "Semi-riemannian geometry"
Hawking & Ellis "The large scale structure of spacetime"
Wald "General relativity"
Lectures notes
Ricevimento: On appointment
PIERRE OLIVIER MARTINETTI (President)
NICOLA PINAMONTI
SIMONE MURRO (President Substitute)
MARCO BENINI (Substitute)
NICOLO' DRAGO (Substitute)
According to the academic calendar
