We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. 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, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.
Dennison, Kenneth A.; Baumgarte, Thomas W.; and Montero, Pedro J., "Trumpet slices in Kerr spacetimes" (2014). Physics Faculty Publications. 89.