732 research outputs found
Radiative Evolution of Orbits Around a Kerr Black Hole
We propose a simple approach for the radiative evolution of generic orbits
around a Kerr black hole. For a scalar-field, we recover the standard results
for the evolution of the energy and the azimuthal angular momentum .
In addition, our method provides a closed expression for the evolution of the
Carter constant .Comment: 6 pages, Plain TeX, Published in Phys. Lett. A. 202, 347 (3 July
1995
Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime
We present a procedure that allows the construction of the metric
perturbations and electromagnetic four-potential, for gravitational and
electromagnetic perturbations produced by sources in Kerr spacetime. This may
include, for example, the perturbations produced by a point particle or an
extended object moving in orbit around a Kerr black hole. The construction is
carried out in the frequency domain. Previously, Chrzanowski derived the vacuum
metric perturbations and electromagnetic four-potential by applying a
differential operator to a certain potential . Here we construct
for inhomogeneous perturbations, thereby allowing the application of
Chrzanowski's method. We address this problem in two stages: First, for vacuum
perturbations (i.e. pure gravitational or electromagnetic waves), we construct
the potential from the modes of the Weyl scalars or .
Second, for perturbations produced by sources, we express in terms of
the mode functions of the source, i.e. the energy-momentum tensor or the electromagnetic current vector .Comment: 20 pages; few typos corrected and minor modifications made; accepted
to Phys. Rev.
A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars I. Construction
R-modes of a rotating neutron star are unstable because of the emission of
gravitational radiation. We explore the saturation amplitudes of these modes
determined by nonlinear mode-mode coupling. Modelling the star as
incompressible allows the analytic computation of the coupling coefficients.
All couplings up to n=30 are obtained, and analytic values for the shear
damping and mode normalization are presented. In a subsequent paper we perform
numerical simulations of a large set of coupled modes.Comment: 15 pages 3 figure
Non-axisymmetric baby-skyrmion branes
We investigate the existence of non axisymmetric solutions in the
6-dimensional baby-Skyrme brane model. The brane is described by a localized
solution to the baby-Skyrme model extending in the extra dimensions. Such non
symmetric branes have already been constructed in the original 2+1-dimensional
baby-Skyrme model in flat space. We generalize this result to the case of
gravitating baby-Skyrme and in the context of extradimensions. These
non-trivial deformation from the axisymmetric shape appear for higher values of
the topological charge, so we consider the cases of , where is the
topological charge. We solve the coupled system of the Einstein and baby-Skyrme
equations by successive over relaxation method. We argue that the result may be
a possible resolution for the fermion mass hierarchy puzzle.Comment: 14 pages, 14 figure
Toward Making the Constraint Hypersurface an Attractor in Free Evolution
There is an abundance of empirical evidence in the numerical relativity
literature that the form in which the Einstein evolution equations are written
plays a significant role in the lifetime of numerical simulations. This paper
attempts to present a consistent framework for modifying any system of
evolution equations by adding terms that push the evolution toward the
constraint hypersurface. The method is, in principle, applicable to any system
of partial differential equations which can be divided into evolution equations
and constraints, although it is only demonstrated here through an application
to the Maxwell equations.Comment: 6 pages, 3 figures, 1 table. Uses REVTeX
Analytic Solutions of Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries
The analytic solution of Teukolsky equation in Kerr-de Sitter and
Kerr-Newman-de Sitter geometries is presented and the properties of the
solution are examined. In particular, we show that our solution satisfies the
Teukolsky-Starobinsky identities explicitly and fix the relative normalization
between solutions with the spin weight and .Comment: 24 pages, LaTe
The Federal Administrative Court Proposal: An Examination of General Principals
Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these featuresâa high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is notâwith geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method
Nonlinear Couplings of R-modes: Energy Transfer and Saturation Amplitudes at Realistic Timescales
Non-linear interactions among the inertial modes of a rotating fluid can be
described by a network of coupled oscillators. We use such a description for an
incompressible fluid to study the development of the r-mode instability of
rotating neutron stars. A previous hydrodynamical simulation of the r-mode
reported the catastrophic decay of large amplitude r-modes. We explain the
dynamics and timescale of this decay analytically by means of a single three
mode coupling. We argue that at realistic driving and damping rates such large
amplitudes will never actually be reached. By numerically integrating a network
of nearly 5000 coupled modes, we find that the linear growth of the r-mode
ceases before it reaches an amplitude of around 10^(-4). The lowest parametric
instability thresholds for the r-mode are calculated and it is found that the
r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included.
Using the network of coupled oscillators, integration times of 10^6 rotational
periods are attainable for realistic values of driving and damping rates.
Complicated dynamics of the modal amplitudes are observed. The initial
development is governed by the three mode coupling with the lowest parametric
instability. Subsequently a large number of modes are excited, which greatly
decreases the linear growth rate of the r-mode.Comment: 3 figures 4 pages Submitted to PR
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