Optical functions in de Sitter
arXiv:1910.05799 · doi:10.1063/5.0049177
Abstract
This paper addresses pure gauge questions in the study of (asymptotically) de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed estimates for the structure coefficients in this gauge. We show two results which are relevant for the foliations used in the stability problem of the expanding region of Schwarzschild de Sitter spacetimes [Schlue (2016)]: (i) Small perturbations of round spheres on the cosmological horizons lead to spheres that pinch off at infinity. (ii) Globally well behaved double null foliations can be constructed from infinity using a choice of spheres related to the level sets of a mass aspect function. While (i) shows that in the above stability problem a final gauge choice is necessary, the proof of (ii) already outlines a strategy for the case of spacetimes with decaying, instead of vanishing, conformal Weyl curvature.
arXiv comment93 pages, 11 figures
References in corpus (14)
- The linear stability of the Schwarzschild solution to gravitational perturbations
- The global non-linear stability of the Kerr-de Sitter family of black holes
- Asymptotics with a positive cosmological constant: I. Basic framework
- A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation
- On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinates
- The cosmological constant and the energy of gravitational radiation
- A positive Bondi--type mass in asymptotically de Sitter spacetimes
- The Hamiltonian mass of asymptotically Schwarzschild-de Sitter space-times
- On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds
- The intersection of a hyperplane with a lightcone in the Minkowski spacetime
- Quasi-local energy with respect to de Sitter/anti-de Sitter reference
- Quasi-local mass at the null infinity of the Vaidya spacetime
- Decay of the Weyl curvature in expanding black hole cosmologies
- Some geometry of de Sitter space