Geometry and Analysis in Black Hole Spacetimes
Black holes play a central role in general relativity and astrophysics. The Kerr solution of the Einstein equations describes a spacetime containing an isolated, rotating black hole. Following a brief introduction to the Cauchy problem for the Einstein equations, I will discuss the main features of the geometry of the Kerr spacetime, including its algebraically special nature and consequences thereof, and some aspects of the Black Hole Stability Problem. Together with closely related Black Hole Uniqueness Problem and the Penrose Inequality, it is one of three major open mathematical problems of general relativity related to the Kerr solution.
Lecturer
Date
6th ~ 20th December, 2022
Website
Prerequisite
Differential Geometry, Riemannian Geometry
Syllabus
Cauchy problem, Kerr solution, 2-spinor formalism, Teukolsky Equation
Audience
Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Lars Andersson is a BIMSA professor. Before joining BIMSA he held professorships at the Royal Institute of Technology, Stockholm, the University of Miami, and led a research group at the Albert Einstein Institute, Potsdam. He works on problems in general relativity, mathematical physics and differential geometry, and has contributed to the mathematical analysis of cosmological models, apparent horizons, and self-gravitating elastic bodies. The recent research interests of Lars Andersson include the black hole stability problem, gravitational instantons, and the gravitational spin Hall effect.