Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. III. On the determination of radiation

Abstract

We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which mimics the physical measurement process. It operates entirely intrisically within $\scri^+$ so that there is no further approximation necessary apart from the basic assumption that the arena be an asymptotically flat space-time. We define the notion of a detector at infinity by idealising local observers in Minkowski space. A detailed discussion is presented for Maxwell fields and the generalisation to linearised and full gravity is performed by way of the similar structure of the asymptotic fields.

LaTeX2e,13 pages,2 figures

References in corpus (3)

• Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. II. The evolution equations
• Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
• How to Avoid Artificial Boundaries in the Numerical Calculation of Black Hole Spacetimes

Cited by in corpus (22)

• Hyperboloidal evolution with the Einstein equations
• Conformal geodesics on vacuum space-times
• Spacelike matching to null infinity
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• A hyperboloidal study of tail decay rates for scalar and Yang-Mills fields
• Numerical relativity with the conformal field equations
• Hyperbolic formulations and numerical relativity: Experiments using Ashtekar's connection variables
• The Hyperboloidal Numerical Evolution of a Good-Bad-Ugly Wave Equation
• Global simulations of Minkowski space-time including space-like infinity
• Stationary hyperboloidal slicings with evolved gauge conditions
• Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space
• The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem
• The numerical initial boundary value problem for the generalized conformal field equations
• Free evolution of the hyperboloidal initial value problem in spherical symmetry
• Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
• Local twistors and the conformal field equations
• Hyperboloidal initial data without logarithmic singularities
• On Killing vectors in initial value problems for asymptotically flat space-times
• Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
• Conformal compactification and affine-null metric formulation of the Einstein equations
• Global versus Local Aspects of Critical Collapse