  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.

General Relativity and Quantum Cosmology