Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices

Abstract

Conformal Carter-Penrose diagrams are used for the visualization of hyperboloidal slices, which are smooth spacelike slices reaching null infinity. The focus is on the Schwarzschild black hole geometry in spherical symmetry, whose Penrose diagrams are introduced in a pedagogical way. The stationary regime involves time-independent slices. In this case, different options are given for integrating the height function -- the main ingredient for constructing hyperboloidal foliations. The dynamical regime considers slices changing in time, which are evolved together with the spacetime using the eikonal equation. It includes the relaxation of hyperboloidal Schwarzschild trumpet slices and the collapse of a massless scalar field into a black hole, for which Penrose diagrams are presented.

18 pages, 14 figures, matches published version

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• Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
• A numerical approach to particle creation in accelerating toy models
• Hyperboloidal approach for linear and non-linear wave equations in FLRW spacetimes
• Charged Scalar Field at Future Null Infinity via Nonlinear Hyperboloidal Evolution
• Hyperboloidal neutron star and black hole initial data in spherical symmetry