2,227 research outputs found
Numerical Integration of Nonlinear Wave Equations for General Relativity
A second-order numerical implementation is given for recently derived
nonlinear wave equations for general relativity. The Gowdy T cosmology is
used as a test bed for studying the accuracy and convergence of simulations of
one-dimensional nonlinear waves. The complete freedom in space-time slicing in
the present formulation is exploited to compute in the Gowdy line-element.
Second-order convergence is found by direct comparison of the results with
either analytical solutions for polarized waves, or solutions obtained from
Gowdy's reduced wave equations for the more general unpolarized waves. Some
directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps
Past and future gauge in numerical relativity
Numerical relativity describes a discrete initial value problem for general
relativity. A choice of gauge involves slicing space-time into space-like
hypersurfaces. This introduces past and future gauge relative to the
hypersurface of present time. Here, we propose solving the discretized Einstein
equations with a choice of gauge in the future and a dynamical gauge in the
past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let
On the origin of exponential growth in induced earthquakes in Groningen
The Groningen gas field shows exponential growth in earthquakes event counts
around a magnitude M1 with a doubling time of 6-9 years since 2001. This
behavior is identified with dimensionless curvature in land subsidence, which
has been evolving at a constant rate over the last few decades {essentially
uncorrelated to gas production.} We demonstrate our mechanism by a tabletop
crack formation experiment. The observed skewed distribution of event
magnitudes is matched by that of maxima of event clusters with a normal
distribution. It predicts about one event \,M5 per day in 2025, pointing to
increasing stress to human living conditions.Comment: 12 pages, 7 figures, to appear in Earthquakes and Structure
Extended black hole cosmologies in de Sitter space
We generalize the superposition principle for time-symmetric initial data of
black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue
problem for a conformal scale
applied to a metric with constant three-curvature . Here,
in the Brill-Lindquist and, respectively, Misner construction of
multihole solutions for . For de Sitter and anti-de Sitter
cosmologies, we express the result for in incomplete elliptic
functions. The topology of a black hole in de Sitter space can be extended into
an infinite tower of universes, across the turning points at the black hole and
cosmological event horizons. Superposition introduces binary black holes for
small separations and binary universes for separations large relative to the
cosmological event horizon. The evolution of the metric can be described by a
hyperbolic system of equations with curvature-driven lapse function, of
alternating sign at successive cosmologies. The computational problem of
interacting black hole-universes is conceivably of interest to early cosmology
when was large and black holes were of mass ,
here facilitated by a metric which is singularity-free and smooth everywhere on
real coordinate space.Comment: to appear in Class. Quant. Gra
Vistas in numerical relativity
Upcoming gravitational wave-experiments promise a window for discovering new
physics in astronomy. Detection sensitivity of the broadband laser
interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with
accurate wave-form templates. Where analytic methods break down, we have to
resort to numerical relativity, often in Hamiltonian or various hyperbolic
formulations. Well-posed numerical relativity requires consistency with the
elliptic constraints of energy and momentum conservation. We explore this using
a choice of gauge in the future and a dynamical gauge in the past. Applied to a
polarized Gowdy wave, this enables solving {\em all} ten vacuum Einstein
equations. Evolution of the Schwarzschild metric in 3+1 and, more generally,
sufficient conditions for well-posed numerical relativity continue to be open
challenges.Comment: invited talk, Asian Pacific CTP Winter School on black hole
astrophysics, Pohang, Kore
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