Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics

Abstract

The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use of information causally connected to an observer. However, the diameter distance, which is used as a radial coordinate, limits the model's cosmological application to the region prior to the PNC refocussing. This is because after refocussing, the diameter distance ceases to be a unique measure of distance. This paper addresses the problem by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced by an affine parameter. A model is derived from this metric and it is then shown how an existing numerical scheme can be adapted for simulation of cosmological PNC behaviour. Numerical calculations on this model are found to have the same stability and convergence properties as the standard characteristic formalism.

18 pages, 9 figures, 1 Table. arXiv admin note: some text overlap with arXiv:some 1007.3189

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Cited by in corpus (8)

• The affine-null metric formulation of Einstein's equations
• The affine-null formulation of the gravitational equations: spherical case
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• What's Inside the Cone? Numerically reconstructing the metric from observations
• Characteristic Formulation for Metric $f(R)$ Gravity
• Towards the geometry of the universe from data
• Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
• Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework