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arXiv · 1403.5484

A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

Kenneth A. Dennison·Thomas W. Baumgarte
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Abstract

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. In the limit $R_{0}=0$ the spatial slices lose their trumpet geometry and become flat -- in this limit, our coordinates reduce to Painlev\'e-Gullstrand coordinates.

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Kenneth A. Dennison, Thomas W. Baumgarte. 2014-03-21. A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime. https://doi.org/10.1088/0264-9381/31/11/117001

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