Conformal geodesics on vacuum space-times

Abstract

We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.

References in corpus (2)

• Bondi-type systems near space-like infinity and the calculation of the NP-constants
• From Now to Timelike Infinity on a Finite Grid

Cited by in corpus (28)

• A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Sharp asymptotics for Einstein-$\lambda$-dust flows
• On de Sitter-like and Minkowski-like space-times
• The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field
• Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
• The Confluent Heun functions in Black Hole Perturbation Theory: a spacetime interpretation
• The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem
• An extension theorem for conformal gauge singularities
• Asymptotic simplicity and static data
• The numerical initial boundary value problem for the generalized conformal field equations
• A rigidity property of asymptotically simple spacetimes arising from conformally flat data
• Is general relativity `essentially understood' ?
• Asymptotics and singularities in cosmological models with positive cosmological constant
• A class of conformal curves in the Reissner-Nordström spacetime
• Analytic conformal compactification of Schwarzschild spacetime
• Spectral methods for the spin-2 equation near the cylinder at spatial infinity
• On the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes
• Conformal actions of nilpotent groups on pseudo-Riemannian manifolds
• Numerical calculations near spatial infinity
• On the non-linear stability of the Cosmological region of the Schwarzschild-de Sitter spacetime
• Conformal geodesics in spherically symmetric vacuum spacetimes with Cosmological constant
• Explorations of the infinite regions of space-time
• A Conformal Extension Theorem based on Null Conformal Geodesics
• Smoothness at null infinity and the structure of initial data
• On the choice of a conformal Gauss gauge near the cylinder representing spatial infinity
• Conformal Einstein evolution
• The non-linear perturbation of a black hole by gravitational waves. I. The Bondi-Sachs mass loss