134 research outputs found
TIME-SYMMETRIC INITIAL DATA SETS IN 4--D DILATON GRAVITY
I study the time--symmetric initial--data problem in theories with a massless
scalar field (dilaton), free or coupled to a Maxwell field in the stringy way,
finding different initial--data sets describing an arbitrary number of black
holes with arbitrary masses, charges and asymptotic value of the dilaton. The
presence of the scalar field gives rise to a number of interesting effects. The
mass and charges of a single black hole are different in its two asymptotically
flat regions across the Einstein--Rosen bridge. The same happens to the value
of the dilaton at infinity. This forbids the identification of these asymptotic
regions in order to build (Misner) wormholes in the most naive way. Using
different techniques, I find regular initial data for stringy wormholes. The
price payed is the existence singularities in the dilaton field. The presence
of a single--valued scalar seems to constrain strongly the allowed topologies
of the initial space--like surface. Other kinds of scalar fields (taking values
on a circle or being defined up to an additive constant) are also briefly
considered.Comment: latex file, 38 pages
The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
Gravitational perturbations about a Kerr black hole in the Newman-Penrose
formalism are concisely described by the Teukolsky equation. New numerical
methods for studying the evolution of such perturbations require not only the
construction of appropriate initial data to describe the collision of two
orbiting black holes, but also to know how such new data must be imposed into
the Teukolsky equation. In this paper we show how Cauchy data can be
incorporated explicitly into the Teukolsky equation for non-rotating black
holes. The Teukolsky function and its first time derivative
can be written in terms of only the 3-geometry and the
extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the
Teukolsky equation incorporates initial data as a source term. We show that for
astrophysical data the straightforward Green function method leads to divergent
integrals that can be regularized like for the case of a source generated by a
particle coming from infinity.Comment: 9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final
version to appear in PR
Time-symmetric initial data for binary black holes in numerical relativity
We look for physically realistic initial data in numerical relativity which
are in agreement with post-Newtonian approximations. We propose a particular
solution of the time-symmetric constraint equation, appropriate to two
momentarily static black holes, in the form of a conformal decomposition of the
spatial metric. This solution is isometric to the post-Newtonian metric up to
the 2PN order. It represents a non-linear deformation of the solution of Brill
and Lindquist, i.e. an asymptotically flat region is connected to two
asymptotically flat (in a certain weak sense) sheets, that are the images of
the two singularities through appropriate inversion transformations. The total
ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are
computed by surface integrals performed at infinity. Using second order
perturbation theory on the Brill-Lindquist background, we prove that the
binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and
in agreement with the known post-Newtonian result.Comment: 27 pages, to appear in Phys. Rev.
A two-mass expanding exact space-time solution
In order to understand how locally static configurations around
gravitationally bound bodies can be embedded in an expanding universe, we
investigate the solutions of general relativity describing a space-time whose
spatial sections have the topology of a 3-sphere with two identical masses at
the poles. We show that Israel junction conditions imply that two spherically
symmetric static regions around the masses cannot be glued together. If one is
interested in an exterior solution, this prevents the geometry around the
masses to be of the Schwarzschild type and leads to the introduction of a
cosmological constant. The study of the extension of the Kottler space-time
shows that there exists a non-static solution consisting of two static regions
surrounding the masses that match a Kantowski-Sachs expanding region on the
cosmological horizon. The comparison with a Swiss-Cheese construction is also
discussed.Comment: 15 pages, 5 figures. Replaced to match the published versio
Estimating the permeability of cement pastes and mortars using image analysis and effective medium theory
Junction Conditions and Consequences of Quasi-Spherical Space-Time with Electro-Magnetic Field and Vaidya Matric
In this work the junction conditions between the exterior
Reissner-Nordstrom-Vaidya space-time with the interior quasi-spherical Szekeres
space-time have been studied for analyzing gravitational collapse in the
presence of a magneto-hydrodynamic fluid undergoing dissipation in the form of
heat flow. We have discussed about the apparent horizon and have evaluated the
time difference between the formation of apparent horizon and central
singularity.Comment: 8 latex pages, RevTex style, no figure
Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering
We present a detailed analytical study of ultra-relativistic neutrinos in
cosmological perturbation theory and of the observable signatures of
inhomogeneities in the cosmic neutrino background. We note that a modification
of perturbation variables that removes all the time derivatives of scalar
gravitational potentials from the dynamical equations simplifies their solution
notably. The used perturbations of particle number per coordinate, not proper,
volume are generally constant on superhorizon scales. In real space an
analytical analysis can be extended beyond fluids to neutrinos.
The faster cosmological expansion due to the neutrino background changes the
acoustic and damping angular scales of the cosmic microwave background (CMB).
But we find that equivalent changes can be produced by varying other standard
parameters, including the primordial helium abundance. The low-l integrated
Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of
neutrino perturbations suppresses the CMB acoustic peaks for the multipoles
with l>~200 while it enhances the amplitude of matter fluctuations on these
scales. In addition, the perturbations of relativistic neutrinos generate a
*unique phase shift* of the CMB acoustic oscillations that for adiabatic
initial conditions cannot be caused by any other standard physics. The origin
of the shift is traced to neutrino free-streaming velocity exceeding the sound
speed of the photon-baryon plasma. We find that from a high resolution, low
noise instrument such as CMBPOL the effective number of light neutrino species
can be determined with an accuracy of sigma(N_nu) = 0.05 to 0.09, depending on
the constraints on the helium abundance.Comment: 38 pages, 7 figures. Version accepted for publication in PR
Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
We present cosmological perturbations of kinetic components based on
relativistic Boltzmann equations in the context of generalized gravity
theories. Our general theory considers an arbitrary number of scalar fields
generally coupled with the gravity, an arbitrary number of mutually interacting
hydrodynamic fluids, and components described by the relativistic Boltzmann
equations like massive/massless collisionless particles and the photon with the
accompanying polarizations. We also include direct interactions among fluids
and fields. The background FLRW model includes the general spatial curvature
and the cosmological constant. We consider three different types of
perturbations, and all the scalar-type perturbation equations are arranged in a
gauge-ready form so that one can implement easily the convenient gauge
conditions depending on the situation. In the numerical calculation of the
Boltzmann equations we have implemented four different gauge conditions in a
gauge-ready manner where two of them are new. By comparing solutions solved
separately in different gauge conditions we can naturally check the numerical
accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.
Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation
Using the 3+1 formalism of general relativity we obtain the equations
governing the dynamics of spherically symmetric spacetimes with arbitrary
sources. We then specialize for the case of perfect fluids accompanied by a
flow of interacting massless or massive particles (e.g. neutrinos) which are
described in terms of relativistic transport theory. We focus in three types of
coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar
slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure
Estimating the permeability of cement pastes and mortars using image analysis and effective medium theory
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