Abstract:
Singularities are a generic feature of Einsteins general theory of relativity. Like the Big Bang, singularities may be present at the initial state of our universe, or develop over time when stars collapse, like black holes. Mathematically such situations occur when a solution to the Einstein equations is geodesically inextendible - there is a void in the universe. In this talk I will review the mechanisms that lead to the
dynamical formation of singularities and discuss the great mathematical challenges that still remain.