Over the Rainbow: Numerical Relativity beyond Scri+

This is a study of the behavior of wave equations in conformally compactified spacetimes suited to the use of computational boundaries beyond Scri+. There light cones may be adjusted for computational convenience and/or Scri+ may be approximated by a "proto-Scri" spacelike hypersurface just outside a de Sitter horizon. One expects a numerical implementation to excise the physically unnecessary universe somewhat beyond the outer horizon. As an entry level example I study forms of the Maxwell equations and causal relations for an outer boundary in that example.Comment: 5 pages, no figures; added acknowledgements and references in v

Spherical Harmonic Decomposition on a Cubic Grid

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In the method described here, the interpolation of the grid data to the integration 2-sphere is combined in the same step as the integrations to extract the spherical harmonic amplitudes, which become sums over grid points. Coordinates adapted to the integration sphere are not needed.Comment: 5 pages, LaTeX uses cjour.cls (supplied

The bigravity black hole and its thermodynamics

We argue that the Isham-Storey exact solution to bigravity does not describe black holes because the horizon is a singular surface. However, this is not a generic property of bigravity, but a property of a particular potential. More general potentials do accept regular black holes. For regular black holes, we compute the total energy and thermodynamical parameters. Phase transitions occur for certain critical temperatures. We also find a novel region on phase space describing up to 4 allowed states for a given temperature.Comment: 14 pages, 9 figure

John Wheeler, relativity, and quantum information

In spring 1952, as John Wheeler neared the end of design work for the first thermonuclear explosion, he plotted a radical change of research direction: from particles and atomic nuclei to general relativity

Excising das All: Evolving Maxwell waves beyond scri

We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity. We exploit this freedom to ensure that all light cones are tilted outward in a region near null infinity, which allows us to impose excision-style boundary conditions in our finite difference code. In this preliminary study we consider electromagnetic waves propagating in a static, conformally compactified spacetime.Comment: 13 pages; incorporated material from gr-qc/051216

Time (in)dependence in general relativity

We clarify the conditions for Birkhoff's theorem, that is, time-independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also derive the equivalence principle. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwell's equations and tensor analysis is required.Comment: Revised version of originally titled "Kinder Kerr", to appear in American Journal of Physic