11,436 research outputs found
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
General Relativistic Scalar Field Models in the Large
For a class of scalar fields including the massless Klein-Gordon field the
general relativistic hyperboloidal initial value problems are equivalent in a
certain sense. By using this equivalence and conformal techniques it is proven
that the hyperboloidal initial value problem for those scalar fields has an
unique solution which is weakly asymptotically flat. For data sufficiently
close to data for flat spacetime there exist a smooth future null infinity and
a regular future timelike infinity.Comment: 22 pages, latex, AGG 1
A Method for Calculating the Structure of (Singular) Spacetimes in the Large
A formalism and its numerical implementation is presented which allows to
calculate quantities determining the spacetime structure in the large directly.
This is achieved by conformal techniques by which future null infinity
(\Scri{}^+) and future timelike infinity () are mapped to grid points on
the numerical grid. The determination of the causal structure of singularities,
the localization of event horizons, the extraction of radiation, and the
avoidance of unphysical reflections at the outer boundary of the grid, are
demonstrated with calculations of spherically symmetric models with a scalar
field as matter and radiation model.Comment: 29 pages, AGG2
Tomographic readout of an opto-mechanical interferometer
The quantum state of light changes its nature when being reflected off a
mechanical oscillator due to the latter's susceptibility to radiation pressure.
As a result, a coherent state can transform into a squeezed state and can get
entangled with the motion of the oscillator. The complete tomographic
reconstruction of the state of light requires the ability to readout arbitrary
quadratures. Here we demonstrate such a readout by applying a balanced homodyne
detector to an interferometric position measurement of a thermally excited
high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout
noise of \unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}} around the
membrane's fundamental oscillation mode at \unit{133}{\kilo\hertz} has been
achieved, going below the peak value of the standard quantum limit by a factor
of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a
rather broad frequency range around the mechanical resonance.Comment: 7 pages, 5 figure
Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations
We study asymptotically constrained systems for numerical integration of the
Einstein equations, which are intended to be robust against perturbative errors
for the free evolution of the initial data. First, we examine the previously
proposed "-system", which introduces artificial flows to constraint
surfaces based on the symmetric hyperbolic formulation. We show that this
system works as expected for the wave propagation problem in the Maxwell system
and in general relativity using Ashtekar's connection formulation. Second, we
propose a new mechanism to control the stability, which we call the ``adjusted
system". This is simply obtained by adding constraint terms in the dynamical
equations and adjusting its multipliers. We explain why a particular choice of
multiplier reduces the numerical errors from non-positive or pure-imaginary
eigenvalues of the adjusted constraint propagation equations. This ``adjusted
system" is also tested in the Maxwell system and in the Ashtekar's system. This
mechanism affects more than the system's symmetric hyperbolicity.Comment: 16 pages, RevTeX, 9 eps figures, added Appendix B and minor changes,
to appear in Class. Quant. Gra
Self-gravitating Klein-Gordon fields in asymptotically Anti-de-Sitter spacetimes
We initiate the study of the spherically symmetric Einstein-Klein-Gordon
system in the presence of a negative cosmological constant, a model appearing
frequently in the context of high-energy physics. Due to the lack of global
hyperbolicity of the solutions, the natural formulation of dynamics is that of
an initial boundary value problem, with boundary conditions imposed at null
infinity. We prove a local well-posedness statement for this system, with the
time of existence of the solutions depending only on an invariant H^2-type norm
measuring the size of the Klein-Gordon field on the initial data. The proof
requires the introduction of a renormalized system of equations and relies
crucially on r-weighted estimates for the wave equation on asymptotically AdS
spacetimes. The results provide the basis for our companion paper establishing
the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this
system.Comment: 50 pages, v2: minor changes, to appear in Annales Henri Poincar\'
Cosmic variance of the galaxy cluster weak lensing signal
Intrinsic variations of the projected density profiles of clusters of
galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We
present a semi-analytical model to account for this effect, based on a
combination of variations in halo concentration, ellipticity and orientation,
and the presence of correlated haloes. We calibrate the parameters of our model
at the 10 per cent level to match the empirical cosmic variance of cluster
profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological
simulation. We show that weak lensing measurements of clusters significantly
underestimate mass uncertainties if intrinsic profile variations are ignored,
and that our model can be used to provide correct mass likelihoods. Effects on
the achievable accuracy of weak lensing cluster mass measurements are
particularly strong for the most massive clusters and deep observations (with
~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol
and z=0.25), but significant also under typical ground-based conditions. We
show that neglecting intrinsic profile variations leads to biases in the
mass-observable relation constrained with weak lensing, both for intrinsic
scatter and overall scale (the latter at the 15 per cent level). These biases
are in excess of the statistical errors of upcoming surveys and can be avoided
if the cosmic variance of cluster profiles is accounted for.Comment: 14 pages, 6 figures; submitted to MNRA
On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity
In Brodbeck et al 1999 it has been shown that the linearised time evolution
equations of general relativity can be extended to a system whose solutions
asymptotically approach solutions of the constraints. In this paper we extend
the non-linear equations in similar ways and investigate the effect of various
possibilities by numerical means. Although we were not able to make the
constraint submanifold an attractor for all solutions of the extended system,
we were able to significantly reduce the growth of the numerical violation of
the constraints. Contrary to our expectations this improvement did not imply a
numerical solution closer to the exact solution, and therefore did not improve
the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
The G_2 sphere over a 4-manifold
We present a construction of a canonical G_2 structure on the unit sphere
tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such
structure is never geometric or 1-flat, but seems full of other possibilities.
We start by the study of the most basic properties of our construction. The
structure is co-calibrated if, and only if, M is an Einstein manifold. The
fibres are always associative. In fact, the associated 3-form results from a
linear combination of three other volume 3-forms, one of which is the volume of
the fibres. We also give new examples of co-calibrated structures on well known
spaces. We hope this contributes both to the knowledge of special geometries
and to the study of 4-manifolds.Comment: 13 page
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