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.

arXiv comment24 pages, 15 figures

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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