The affine-null formulation of the gravitational equations: spherical case

Abstract

A new evolution algorithm for the characteristic initial value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation is applied in the spherically symmetric case to the gravitational collapse of a massless scalar field. The advantages over the Bondi-Sachs version are discussed, with particular emphasis on the application to critical collapse. Unexpected quadratures lead to a simple evolution algorithm based upon ordinary differential equations which can be integrated along the null rays. For collapse to a black hole in a Penrose compactified spacetime, these equations are regularized throughout the exterior and interior of the horizon up to the final singularity. They are implemented as a global numerical evolution code based upon the Galerkin method. New results regarding the global properties of critical collapse are presented.

arXiv comment18 pages, 10 figures

References in corpus (13)

• Critical phenomena in gravitational collapse
• High-powered Gravitational News
• Bondi-Sachs Formalism
• Understanding critical collapse of a scalar field
• The spherically symmetric collapse of a massless scalar field
• Choptuik scaling in null coordinates
• Critical phenomena in gravitational collapse - Living Reviews
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• The affine-null metric formulation of Einstein's equations
• Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method
• The naked singularity in the global structure of critical collapse spacetimes
• Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics

Cited by in corpus (13)

• Hyperbolicity of General Relativity in Bondi-like gauges
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field
• Numerical convergence of model Cauchy-characteristic extraction and matching
• Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
• The Bondi problem revisited: a spectral domain decomposition code
• Multidomain Galerkin-Collocation method: characteristic spherical collapse of scalar fields
• Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
• Multidomain Galerkin-Collocation method: spherical collapse of scalar fields II
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Conformal compactification and affine-null metric formulation of the Einstein equations
• Spherically symmetric black holes and affine-null metric formulation of Einstein's equations
• Hierarchical formulation of the self-gravitating, n-dimensional, charged scalar field in spherical symmetry in affine null formalism