Beyond circles: stationary axisymmetric black holes and the breaking of circularity

Circularity is an accidental symmetry of the Kerr metric, one that is widely assumed when searching for rotating black hole solutions in modified gravity as well as when constructing models of Kerr mimickers. Though extremely enticing, circularity is often an excessively restrictive assumption, and understanding the consequences of its loss is thus crucially relevant. In this seminar, I wish to present some recent results on the subject: After describing in detail what this symmetry entails, I will show how to construct stationary and axisymmetric spacetimes exhibiting a controlled breaking of circularity; then, I will describe the impact of circularity breaking on the hole’s horizon, focusing in particular on the laws of black hole mechanics. This discussion is thus going to be pertinent for anyone with an interest in compact astrophysical objects and their phenomenology, in general relativity and beyond.