Black holes, the big bang, and spacetime singularities

Abstract:  Two of the most exotic consequences of general relativity are black holes and the big bang. And yet there is abundant astrophysical evidence for both of these phenomena. This talk will cover the properties of black holes and the big bang, with particular focus on spacetime singularities: the idea that deep within black hole interiors and at the earliest moments of the universe the curvature of spacetime becomes arbitrarily large. We will cover the Penrose singularity theorem and then use a combination of analytical and numerical methods to understand the properties of singularities.