5,813 research outputs found
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
Taub-NUT space as a counterexample to almost anything Technical report no. 529
Taub-NUT space as countermeasure to almost anything - Einstein equation, classical mechanics, and differential equation
Integration over connections in the discretized gravitational functional integrals
The result of performing integrations over connection type variables in the
path integral for the discrete field theory may be poorly defined in the case
of non-compact gauge group with the Haar measure exponentially growing in some
directions. This point is studied in the case of the discrete form of the first
order formulation of the Einstein gravity theory. Here the result of interest
can be defined as generalized function (of the rest of variables of the type of
tetrad or elementary areas) i. e. a functional on a set of probe functions. To
define this functional, we calculate its values on the products of components
of the area tensors, the so-called moments. The resulting distribution (in
fact, probability distribution) has singular (-function-like) part with
support in the nonphysical region of the complex plane of area tensors and
regular part (usual function) which decays exponentially at large areas. As we
discuss, this also provides suppression of large edge lengths which is
important for internal consistency, if one asks whether gravity on short
distances can be discrete. Some another features of the obtained probability
distribution including occurrence of the local maxima at a number of the
approximately equidistant values of area are also considered.Comment: 22 page
Quantum nature of black holes
I reconsider Hawking's analysis of the effects of gravitational collapse on
quantum fields, taking into account interactions between the fields. The
ultra-high energy vacuum fluctuations, which had been considered to be an
awkward peripheral feature of the analysis, are shown to play a key role. By
interactions, they can scatter particles to, or create pairs of particle at,
ultra-high energies. The energies rapidly become so great that quantum gravity
must play a dominant role. Thus the vicinities of black holes are essentially
quantum-gravitational regimes.Comment: 7 pages, 5 figures. Honorable mention in the 2004 Gravity Research
Foundation Essay Competitio
Exact Cosmological Solutions of Gravitational Theories
A global picture is drawn tying together most exact cosmological solutions of
gravitational theories in four or more spacetime dimensions.Comment: 11 latex article style page
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