A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

Understand

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 $R_0$ (with $0<R_{0}\leq M$) that serves as the free parameter for the family.
• The slices also have an asymptotically flat end at spatial infinity.