8,588 research outputs found
Dynamical evolution of unstable self-gravitating scalar solitons
Recently, static and spherically symmetric configurations of globally regular
self-gravitating scalar solitons were found. These configurations are unstable
with respect to radial linear perturbations. In this paper we study the
dynamical evolution of such configurations and show that, depending on the sign
of the initial perturbation, the solitons either collapse to a Schwarzschild
black hole or else ``explode'' into an outward moving domain wall.Comment: 11 pages, 16 figures, submitted to Phys. Rev.
Conformal ``thin sandwich'' data for the initial-value problem of general relativity
The initial-value problem is posed by giving a conformal three-metric on each
of two nearby spacelike hypersurfaces, their proper-time separation up to a
multiplier to be determined, and the mean (extrinsic) curvature of one slice.
The resulting equations have the {\it same} elliptic form as does the
one-hypersurface formulation. The metrical roots of this form are revealed by a
conformal ``thin sandwich'' viewpoint coupled with the transformation
properties of the lapse function.Comment: 7 pages, RevTe
Hyperbolicity and Constrained Evolution in Linearized Gravity
Solving the 4-d Einstein equations as evolution in time requires solving
equations of two types: the four elliptic initial data (constraint) equations,
followed by the six second order evolution equations. Analytically the
constraint equations remain solved under the action of the evolution, and one
approach is to simply monitor them ({\it unconstrained} evolution). Since
computational solution of differential equations introduces almost inevitable
errors, it is clearly "more correct" to introduce a scheme which actively
maintains the constraints by solution ({\it constrained} evolution). This has
shown promise in computational settings, but the analysis of the resulting
mixed elliptic hyperbolic method has not been completely carried out. We
present such an analysis for one method of constrained evolution, applied to a
simple vacuum system, linearized gravitational waves.
We begin with a study of the hyperbolicity of the unconstrained Einstein
equations. (Because the study of hyperbolicity deals only with the highest
derivative order in the equations, linearization loses no essential details.)
We then give explicit analytical construction of the effect of initial data
setting and constrained evolution for linearized gravitational waves. While
this is clearly a toy model with regard to constrained evolution, certain
interesting features are found which have relevance to the full nonlinear
Einstein equations.Comment: 18 page
Extrinsic Curvature and the Einstein Constraints
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian)
representation and conformal thin sandwich (Lagrangian) representation are
brought into complete conformity by the use of a decomposition of symmetric
tensors which involves a weight function. In stationary spacetimes, there is a
natural choice of the weight function such that the transverse traceless part
of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex
Scale-invariant gravity: Spacetime recovered
The configuration space of general relativity is superspace - the space of
all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued
that the configuration space for gravity should be conformal superspace - the
space of all Riemannian 3-metrics modulo diffeomorphisms and conformal
transformations. Recently a manifestly 3-dimensional theory was constructed
with conformal superspace as the configuration space. Here a fully
4-dimensional action is constructed so as to be invariant under conformal
transformations of the 4-metric using general relativity as a guide. This
action is then decomposed to a (3+1)-dimensional form and from this to its
Jacobi form. The surprising thing is that the new theory turns out to be
precisely the original 3-dimensional theory. The physical data is identified
and used to find the physical representation of the theory. In this
representation the theory is extremely similar to general relativity. The
clarity of the 4-dimensional picture should prove very useful for comparing the
theory with those aspects of general relativity which are usually treated in
the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex
No-go theorem for bimetric gravity with positive and negative mass
We argue that the most conservative geometric extension of Einstein gravity
describing both positive and negative mass sources and observers is bimetric
gravity and contains two copies of standard model matter which interact only
gravitationally. Matter fields related to one of the metrics then appear dark
from the point of view of an observer defined by the other metric, and so may
provide a potential explanation for the dark universe. In this framework we
consider the most general form of linearized field equations compatible with
physically and mathematically well-motivated assumptions. Using gauge-invariant
linear perturbation theory, we prove a no-go theorem ruling out all bimetric
gravity theories that, in the Newtonian limit, lead to precisely opposite
forces on positive and negative test masses.Comment: 19 pages, no figures, journal versio
Excision boundary conditions for black hole initial data
We define and extensively test a set of boundary conditions that can be
applied at black hole excision surfaces when the Hamiltonian and momentum
constraints of general relativity are solved within the conformal thin-sandwich
formalism. These boundary conditions have been designed to result in black
holes that are in quasiequilibrium and are completely general in the sense that
they can be applied with any conformal three-geometry and slicing condition.
Furthermore, we show that they retain precisely the freedom to specify an
arbitrary spin on each black hole. Interestingly, we have been unable to find a
boundary condition on the lapse that can be derived from a quasiequilibrium
condition. Rather, we find evidence that the lapse boundary condition is part
of the initial temporal gauge choice. To test these boundary conditions, we
have extensively explored the case of a single black hole and the case of a
binary system of equal-mass black holes, including the computation of
quasi-circular orbits and the determination of the inner-most stable circular
orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference,
minor content changes including additional post-Newtonian comparison. Version
accepted by PR
Conformal thin-sandwich puncture initial data for boosted black holes
We apply the puncture approach to conformal thin-sandwich black-hole initial
data. We solve numerically the conformal thin-sandwich puncture (CTSP)
equations for a single black hole with non-zero linear momentum. We show that
conformally flat solutions for a boosted black hole have the same maximum
gravitational radiation content as the corresponding Bowen-York solution in the
conformal transverse-traceless decomposition. We find that the physical
properties of these data are independent of the free slicing parameter.Comment: 12 pages, 11 figure
Large Scale Structure Forecast Constraints on Particle Production During Inflation
Bursts of particle production during inflation provide a well-motivated
mechanism for creating bump like features in the primordial power spectrum.
Current data constrains these features to be less than about 5% the size of the
featureless primordial power spectrum at wavenumbers of about 0.1 h Mpc^{-1}.
We forecast that the Planck cosmic microwave background experiment will be able
to strengthen this constraint to the 0.5% level. We also predict that adding
data from a square kilometer array (SKA) galaxy redshift survey would improve
the constraint to about the 0.1% level. For features at larger wave-numbers,
Planck will be limited by Silk damping and foregrounds. While, SKA will be
limited by non-linear effects. We forecast for a Cosmic Inflation Probe (CIP)
galaxy redshift survey, similar constraints can be achieved up to about a
wavenumber of 1 h Mpc^{-1}.Comment: 10 pages. Matches PRD accepted versio
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