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 $B=3,4$, where $B$ 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

On the Stability of the Iterated Crank-Nicholson Method in Numerical Relativity

The iterated Crank-Nicholson method has become a popular algorithm in numerical relativity. We show that one should carry out exactly two iterations and no more. While the limit of an infinite number of iterations is the standard Crank-Nicholson method, it can in fact be worse to do more than two iterations, and it never helps. We explain how this paradoxical result arises

Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity

Neutron stars in binary orbit emit gravitational waves and spiral slowly together. During this inspiral, they are expected to have very little vorticity. It is in fact a good approximation to treat the system as having zero vorticity, i.e., as irrotational. Because the orbital period is much shorter than the radiation reaction time scale, it is also an excellent approximation to treat the system as evolving through a sequence of equilibrium states, in each of which the gravitational radiation is neglected. In Newtonian gravity, one can simplify the hydrodynamic equations considerably for an equilibrium irrotational binary by introducing a velocity potential. The equations reduce to a Poisson-like equation for the potential, and a Bernoulli-type integral for the density. We show that a similar simplification can be carried out in general relativity. The resulting equations are much easier to solve than other formulations of the problem.Comment: 14 pages, AASTeX, accepted in ApJ. Simplified final form of equation (eq. 52). Added Shibata re

Late-Time Evolution of Charged Gravitational Collapse and Decay of Charged Scalar Hair - II

We study analytically the initial value problem for a charged massless scalar-field on a Reissner-Nordstr\"om spacetime. Using the technique of spectral decomposition we extend recent results on this problem. Following the no-hair theorem we reveal the dynamical physical mechanism by which the charged hair is radiated away. We show that the charged perturbations decay according to an inverse power-law behaviour at future timelike infinity and along future null infinity. Along the future outer horizon we find an oscillatory inverse power-law relaxation of the charged fields. We find that a charged black hole becomes ``bald'' slower than a neutral one, due to the existence of charged perturbations. Our results are also important to the study of mass-inflation and the stability of Cauchy horizons during a dynamical gravitational collapse of charged matter in which a charged black-hole is formed.Comment: Latex 15 pages, Revtex.st

A scalar hyperbolic equation with GR-type non-linearity

We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and non-linear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time $t$ when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when $t$ is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and non-linear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy and convergence at finite $t$ do not guarantee a correct asymptotic behavior and long-term numerical stability. Accuracy and stability of integration are greatly improved by an exponential transformation of the unknown variable.Comment: submitted to Class. Quantum Gra

Equilibrium and stability of relativistic cylindrical polytropes

We examine the structure and radial stability of infinitely long cylindrical polytropes in general relativity. We show that in contrast with spherical polytropes, all cylindrical polytropes are stable. Thus pressure regeneration is not decisive in determining the behavior of cylindrical systems. We discuss how the behavior of infinite cylinders is qualitatively different from that of finite, asymptotically flat configurations. We argue that the use of infinite cylinders to gain physical insight into the collapse of finite aspherical systems may be misleading. In particular, the ability of pressure and rotation to always halt the collapse of an infinite cylinder to a naked singularity may not carry over to finite systems

Eclipse mechanisms for binary pulsars

The parameters of the new eclipsing millisecond pulsar PSR 1744 - 24A in Terzan 5 are sufficiently different from those of PSR 1957 + 20 that very severe constraints can be put now on the theoretical models and formation scenarios of such systems. Most importantly, the eclipse cannot be caused by refractive effects (either total reflection or bending of the radio signal paths). Instead, they very likely are produced by an absorption mechanism, possibly combined with pulse-smearing effects. A model based on free-free absorption by the gas evaporated from the companion remains viable in spite of difficulties. Independent of the particular eclipse mechanism, the results of some preliminary dynamical calculations of the evaporative flow are discussed