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

P. J. van der Walt and N. T. Bishop
Phys. Rev. D 85, 044016 – Published 7 February 2012

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 refocusing. This is because after refocusing, 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 behavior. Numerical calculations on this model are found to have the same stability and convergence properties as the standard characteristic formalism.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 25 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.044016

© 2012 American Physical Society

Authors & Affiliations

P. J. van der Walt and N. T. Bishop

  • Department of Mathematics, Rhodes University, Grahamstown 6140, South Africa

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 85, Iss. 4 — 15 February 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×