We describe a simple family of analytical coordinate systems for the Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are spatially isotropic. Spatial slices of constant coordinate time t feature a trumpet geometry with an asymptotically cylindrical end inside the horizon at a prescribed areal radius R0 (with 0 < R0 M) that serves as the free parameter for the family. The slices also have an asymptotically flat end at spatial infinity. In the limit R0 = 0 the spatial slices lose their trumpet geometry and become flat - in this limit, our coordinates reduce to Painlevé- Gullstrand coordinates. © 2014 IOP Publishing Ltd.
Dennison, Kenneth A. and Baumgarte, Thomas W., "A simple family of analytical trumpet slices of the Schwarzschild spacetime" (2014). Physics Faculty Publications. 90.