Hyperbolic times in Minkowski space

Abstract

Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black-hole perturbations to analyzing wave equations. Despite their significance, many of their properties remain underexplored. In this expository article, I discuss hyperbolic time functions by considering the hyperbola as the relativistic analog of a circle in two-dimensional Minkowski space and argue that suitably defined hyperboloidal coordinates are as natural in Lorentzian manifolds as spherical coordinates are in Riemannian manifolds.

24 pages, 15 figures

References in corpus (7)

• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Hyperboloidal foliations and scri-fixing
• The general spherically symmetric constant mean curvature foliations of the Schwarzschild solution
• Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime
• Excising das All: Evolving Maxwell waves beyond scri
• Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices
• The ďAlembert solution in hyperboloidal foliations

Cited by in corpus (7)

• Hyperboloidal Approach to Quasinormal Modes
• Quasi-normal mode expansions of black hole perturbations: a hyperboloidal Keldysh's approach
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Pseudospectrum and time-domain analysis of the EFT corrected black holes
• The ďAlembert solution in hyperboloidal foliations
• QNM families: classification and competition
• Hyperboloidal approach for linear and non-linear wave equations in FLRW spacetimes