Description
The Kerr metric enjoys a special symmetry known as circularity, which is normally assumed when constructing rotating black hole solutions in alternative theories of gravity and when building Kerr-mimicker models. In this talk I will examine how justified this assumption is and what happens when it breaks. Working within a geometrically natural gauge, the circularity conditions are solved analytically and translated into algebraic relations among metric components, enabling controlled study of circularity-breaking deformations. Explicit analytical examples of non-circular Kerr deformations are presented, highlighting how the horizon can lose its Killing nature even when its location and the ergosphere remain unchanged. These results lay the groundwork for more general parametrizations of rotating black holes and their observational signatures beyond general relativity.