Analytical Trumpet Slices in Schwarzschild and Kerr Spacetimes

We will start by presenting a new family of coordinate systems for the Schwarzschild spacetime. These remarkably simple coordinates have some other remarkable properties as well, including the fact that slices of constant time feature a trumpet geometry. Moreover, these coordinates can be generalized for rotating black holes, resulting in a new family of coordinate systems for Kerr spacetimes. We will then introduce a 2+1+1 formalism to characterize trumpet geometries in the absence of spherical symmetry. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes.