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We describe a simple family of analytical coordinate systems for theSchwarzschild spacetime. The coordinates penetrate the horizon smoothly and arespatially isotropic. Spatial slices of constant coordinate time $t$ feature atrumpet geometry with an asymptotically cylindrical end inside the horizon at aprescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the freeparameter for the family. The slices also have an asymptotically flat end atspatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpetgeometry and become flat -- in this limit, our coordinates reduce toPainlev\'e-Gullstrand coordinates.

A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime