39,526 research outputs found
BSSN in Spherical Symmetry
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein
evolution equations is written in spherical symmetry. These equations can be
used to address a number of technical and conceptual issues in numerical
relativity in the context of a single Schwarzschild black hole. One of the
benefits of spherical symmetry is that the numerical grid points can be tracked
on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture
evolution of a Schwarzschild black hole are presented. Several results are
shown for puncture evolution using a fourth--order finite difference
implementation of the equations.Comment: This is the final version to be published in CQG. It contains much
more information and detail than the original versio
Gravitational Energy in Spherical Symmetry
Various properties of the Misner-Sharp spherically symmetric gravitational
energy E are established or reviewed. In the Newtonian limit of a perfect
fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic
and potential energy to the next order. For test particles, the corresponding
Hajicek energy is conserved and has the behaviour appropriate to energy in the
Newtonian and special-relativistic limits. In the small-sphere limit, the
leading term in E is the product of volume and the energy density of the
matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial
infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies
respectively. The conserved Kodama current has charge E. A sphere is trapped if
E>r/2, marginal if E=r/2 and untrapped if E<r/2, where r is the areal radius. A
central singularity is spatial and trapped if E>0, and temporal and untrapped
if E<0. On an untrapped sphere, E is non-decreasing in any outgoing spatial or
null direction, assuming the dominant energy condition. It follows that E>=0 on
an untrapped spatial hypersurface with regular centre, and E>=r_0/2 on an
untrapped spatial hypersurface bounded at the inward end by a marginal sphere
of radius r_0. All these inequalities extend to the asymptotic energies,
recovering the Bondi-Sachs energy loss and the positivity of the asymptotic
energies, as well as proving the conjectured Penrose inequality for black or
white holes. Implications for the cosmic censorship hypothesis and for general
definitions of gravitational energy are discussed.Comment: 23 pages. Belatedly replaced with substantially extended published
versio
Strengths of singularities in spherical symmetry
Covariant equations characterizing the strength of a singularity in spherical
symmetry are derived and several models are investigated. The difference
between central and non-central singularities is emphasised. A slight
modification to the definition of singularity strength is suggested. The
gravitational weakness of shell crossing singularities in collapsing spherical
dust is proven for timelike geodesics, closing a gap in the proof.Comment: 16 pages, revtex. V2. Classification of irregular singular points
completed, Comments and references on singularities with a continuous metric
amende
Transverse-Momentum Distributions and Spherical Symmetry
Transverse-momentum dependent parton distributions (TMDs) are studied in the
framework of quark models. In particular, quark model relations among TMDs are
reviewed and their physical origin is discussed in terms of rotational-symmetry
properties of the nucleon state in its rest frame.Comment: 8 pages, 2 figures, prepared for the workshop "30 years of strong
interactions", Spa, Belgium, 6-8 April 201
Generalized harmonic formulation in spherical symmetry
In this pedagogically structured article, we describe a generalized harmonic
formulation of the Einstein equations in spherical symmetry which is regular at
the origin. The generalized harmonic approach has attracted significant
attention in numerical relativity over the past few years, especially as
applied to the problem of binary inspiral and merger. A key issue when using
the technique is the choice of the gauge source functions, and recent work has
provided several prescriptions for gauge drivers designed to evolve these
functions in a controlled way. We numerically investigate the parameter spaces
of some of these drivers in the context of fully non-linear collapse of a real,
massless scalar field, and determine nearly optimal parameter settings for
specific situations. Surprisingly, we find that many of the drivers that
perform well in 3+1 calculations that use Cartesian coordinates, are
considerably less effective in spherical symmetry, where some of them are, in
fact, unstable.Comment: 47 pages, 15 figures. v2: Minor corrections, including 2 added
references; journal version
Testing for Bivariate Spherical Symmetry
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good perfor- mance of the test is demonstrated. Furthermore, a real data example is presented.Asymptotic distribution;distribution-free;empirical like- lihood;hypothesis test;spherical symmetry.
Spherical symmetry in -gravity
Spherical symmetry in gravity is discussed in details considering also
the relations with the weak field limit. Exact solutions are obtained for
constant Ricci curvature scalar and for Ricci scalar depending on the radial
coordinate. In particular, we discuss how to obtain results which can be
consistently compared with General Relativity giving the well known
post-Newtonian and post-Minkowskian limits. Furthermore, we implement a
perturbation approach to obtain solutions up to the first order starting from
spherically symmetric backgrounds. Exact solutions are given for several
classes of theories in both constant and .Comment: 13 page
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