Black hole uniqueness and related problems in geometric analysis

In the recent observations of black holes, astronomers looked for and found black holes modeled by the Kerr spacetime, predicted by Kerr in 1963.

The question that arises is: Can there be other kinds of black holes, different from the ones mathematically discovered by Kerr? Remarkably, this fundamental question has not yet been answered.

Though it is often claimed that Stephen Hawking in 1972 proved that no other black holes are possible, his proof is mathematically incomplete.

Filling this gap has since been an important problem in mathematical general relativity, known as the black hole uniqueness conjecture.

During several decades, attempts to solve it have developed and connected various different topics in geometric analysis. This conjecture, and related problems in geometric analysis revolving around it, is the core of the project proposal.

The PI (Oliver Lindblad Petersen) will work on this project over a period of four years.We plan to attack the problem via methods in modern microlocal analysis, which has not been done before.

Concretely, we outline a strategy based on new analytic hypoellipticity results and propagation of analytic singularity/regularity (in the sense of Hörmander).

This is significantly different from the standard approach initiated by Alexakis, Ionescu and Klainerman, based on unique continuation for wave equations, a method which has so far been insufficient.