A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

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 $0<R_0\le M$) 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 Painlevé-Gullstrand coordinates.

7 pages, 3 figures

References in corpus (3)

• Geometry and Regularity of Moving Punctures
• Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation
• Analytical Representation of a Black Hole Puncture Solution

Cited by in corpus (10)

• Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics
• Gauge preheating with full general relativity
• Trumpet Slices in Kerr Spacetimes
• Spherically symmetric black hole spacetimes on hyperboloidal slices
• Bona-Masso slicing conditions and the lapse close to black-hole punctures
• Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices
• Bondi Accretion in Trumpet Geometries
• Dynamical perturbations of black-hole punctures: effects of slicing conditions
• Bona-Massó slices of Reissner-Nordström spacetimes
• Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries