Recent Progress in General Relativity

Explore recent advancements in General Relativity through this 45-minute lecture by Gustav Holzegel and Peter Hintz, presented by the International Mathematical Union. Delve into Lorentzian manifolds, Einstein Equations, and the fundamental theorem of general relativity. Examine well-posed systems of PDEs, maximally symmetric solutions, and their stability. Investigate black hole solutions, perturbations, and toy stability models. Gain insights into non-linear stability proofs, the black hole interior, and developments in many-black-hole spacetimes. Enhance your understanding of cutting-edge research in this complex field of physics and mathematics.

Intro
General Relativity I: Lorentzian manifolds
General Relativity II: The Einstein Equations (1915)
The "fundamental theorem" of general relativity
Writing the EVE as a well-posed system of PDES
Exact solutions I: The maximally symmetric solutions
Stability of the maximally symmetric solutions I: A20
Stability of the maximally symmetric solutions II: ACOL
Exact solutions lla: Black hole solutions
Perturbations of black holes
Toy stability 1: decay
Toy stability II: asymptotics, lower bounds
Some ideas and techniques in the proofs
Non-linear stability (A -0)
Comments about the proof
Non-linear stability (A 0)
A quick glance at the dark side I: the black hole interior
Other developments II: many-black-hole spacetimes