arXiv subjects

Patricio S. Letelier

Publications and source records attributed to Patricio S. Letelier.

At least 37 records · Page 2Linked to original sources

arXiv2007

Stability of Closed Timelike Curves in Goedel Universe

We study, in some detail, the linear stability of closed timelike curves in the Goedel metric. We show that these curves are stable. We present a simple extension (deformation) of the Goedel metric that contains a class of closed timelike curves similar to the ones associated to the original Goedel metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in Goedel universe with or whithout the inclusion of regular or exotic matter are also stable under linear perturbations. We also find a sort of structural stability.

gr-qc↗

arXiv2007

Triaxial Analytical Potential-Density Pairs for Galaxies

We present two triaxial analytical potential-density pairs that can be viewed as generalized versions of the axisymmetric Miyamoto and Nagai and Satoh galactic models. These potential-density pairs may be useful models for galaxies with box-shaped bulges. The resulting mass density distributions are everywhere non-negative and free from singularities. Also, a few numerically calculated orbits for the Miyamoto and Nagai-like triaxial potential are presented.

astro-ph↗

arXiv2006

Numeric simulation of relativistic stellar core collapse and the formation of Reissner-Nordstrom space-times

The time evolution of a set of 22 Mo unstable charged stars that collapse is computed integrating the Einstein-Maxwell equations. The model simulate the collapse of an spherical star that had exhausted its nuclear fuel and have or acquires a net electric charge in its core while collapsing. When the charge to mass ratio is Q/M >= 1 the star do not collapse and spreads. On the other hand, it is observed a different physical behavior with a charge to mass ratio 1 > Q/ M > 0.1. In this case, the collapsing matter forms a bubble enclosing a lower density core. We discuss an immediate astrophysical consequence of these results that is a more efficient neutrino trapping during the stellar collapse and an alternative mechanism for powerful supernova explosions. The outer space-time of the star is the Reissner-Nordstrom solution that match smoothly with our interior numerical solution, thus the collapsing models forms Reissner-Nordstrom black holes.

astro-ph↗

arXiv2006

Stability of general relativistic static thick disks: the isotropic Schwarzschild thick disk

We study the stability of general relativistic static thick disks, as an application we consider the thick disk generated by applying the ``displace, cut, fill and reflect" method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates. The isotropic Schwarzschild thick disk obtained from this method is the simplest model to describe, in the context of General Relativity, real thick galaxies. The stability under a general first order perturbation of the disk is investigated. The first order perturbation, when applying to the conservation equations, leads to a set of differential equations that are, in general, not self-consistent. This opens the possibility of performing various kinds of perturbations to transform the resulting system of equations into a self-consistent system. We perform a complete classification of the perturbations as well as the stability analysis for all the relevant physical perturbations. We found that, in general, the isotropic Schwarzschild thick disk is stable under these kinds of perturbations.

gr-qc↗

arXiv2005

Solving procedure for a twenty-five diagonal coefficient matrix: direct numerical solutions of the three dimensional linear Fokker-Planck equation

We describe an implicit procedure for solving linear equation systems resulting from the discretization of the three dimensional (seven variables) linear Fokker-Planck equation. The discretization of the Fokker-Planck equation is performed using a twenty-five point molecule that leads to a coefficient matrix with equal number of diagonals. The method is an extension of Stone's implicit procedure, includes a vast class of collision terms and can be applied to stationary or non stationary problems with different discretizations in time. Test calculations and comparisons with other methods are presented in two stationary examples, including an astrophysical application for the Miyamoto-Nagai disk potential for a typical galaxy.

physics.comp-ph↗

arXiv2005

Motion of a Particle with Isospin in the Presence of a Monopole

From a consistent expression for the quadriforce describing the interaction between a coloured particle and gauge fields, we investigate the relativistic motion of a particle with isospin interacting with a BPS monopole and with a Julia-Zee dyon. The analysis of such systems reveals the existence of unidimensional unbounded motion and asymptotic trajectories restricted to conical surfaces, which resembles the equivalent case of Electromagnetism.

hep-th↗

arXiv2005

Numerical self-consistent stellar models of thin disks

We find a numerical self-consistent stellar model by finding the distribution function of a thin disk that satisfies simultaneously the Fokker-Planck and Poisson equations. The solution of the Fokker-Planck equation is found by a direct numerical solver using finite differences and a variation of Stone's method. The collision term in the Fokker-Planck equation is found using the local approximation and the Rosenbluth potentials. The resulting diffusion coefficients are explicitly evaluated using a Maxwellian distribution for the field stars. As a paradigmatic example, we apply the numerical formalism to find the distribution function of a Kuzmin-Toomre thin disk. This example is studied in some detail showing that the method applies to a large family of actual galaxies.

astro-ph↗

arXiv2004

Motion of Coloured Particles in Solitons of the O(3) Non-Linear Model

We propose a consistent expression for the relativistic quadri-force referring to the classical interaction between a coloured particle and a scalar field multiplete. General aspects of the resultant equations of motion are discussed as well as a specialisation to the case of a SU(2) particle in the presence of a soliton configuration of the non-linear O(3) model with unit topological charge. Analytical studies regarding the stability and asymptotic behaviour of this system are made and extended to the case of arbitrary topological charge. Since the non-linear O(3) model describes an isotropic ferromagnet, we also investigate a possible physical interpretation of such a system.

hep-th↗

arXiv2004

On the stability of general relativistic geometric thin disks

The stability of general relativistic thin disks is investigated under a general first order perturbation of the energy momentum tensor. In particular, we consider temporal, radial and azimuthal "test matter" perturbations of the quantities involved on the plane $z=0$. We study the thin disks generated by applying the "displace, cut and reflect" method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates and to the Chazy-Curzon metric and the Zipoy-Voorhees metric ($γ$-metric) in Weyl coordinates. In the case of the isotropic Schwarzschild thin disk, where a radial pressure is present to support the gravitational attraction, the disk is stable and the perturbation favors the formation of rings. Also, we found the expected result that the thin disk models generated by the Chazy-Curzon and Zipoy-Voorhees metric with only azimuthal pressure are not stable under a general first order perturbation

gr-qc↗

arXiv2004

Space-Time geometry and thermodynamic properties of a self-gravitating ball of fluid in phase transition

A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the internal interactions of the system are represented by a van der Walls like equation of state able to describe a first order phase transition of the type gas-liquid. We find that the space-time curvature, the radial component of the metric, and the pressure and density show discontinuities in their radial derivatives in the phase coexistence region. This region is found to be a spherical surface concentric with the star and the system can be thought as a foliation of acronal, concentric and isobaric surfaces in which the coexistence of phases occurs in only one of these surfaces. This kind of system can be used to represent a star with a high energy density core and low energy density mantle in hydrodynamic equilibrium.

gr-qc↗

arXiv2003

Numerical Simulation of General Relativistic Stellar Collapse

We present preliminar results and tests of a new general relativistic code to simulate the hydrodynamic collapse of a 21 solar masses star. We have assumed spherical symmetry and used the formalism of Misner and Sharp to construct a finite-difference scheme to solve the Einstein's equations, energy-momentum conservation equations and baryonic conservation equation. The code is similar to the one originally developed by May and White (1967). Here we discuss the capabilities of the code that make it well suited for numerical relativity on a personal computer and some caveats based on the experiments we have made with it.

gr-qc↗

arXiv2003

Exact General Relativistic Thick Disks

A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a ``displace, cut, {\it fill} and reflect'' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have non trivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.

gr-qc↗

arXiv2003

Exact General Relativistic Perfect Fluid Disks with Halos

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic coordinates. The same method is applied to different exactsolutions to the Einstein'sequations that represent static spheres of perfect fluids. We construct several models of disks with axially symmetric perfect fluid halos. All disks have some common features: surface energy density and pressures decrease monotonically and rapidly with radius. As the ``cut'' parameter $a$ decreases, the disks become more relativistic, with surface energy density and pressure more concentrated near the center. Also regions of unstable circular orbits are more likely to appear for high relativistic disks. Parameters can be chosen so that the sound velocity in the fluid and the tangential velocity of test particles in circular motion are less then the velocity of light. This tangential velocity first increases with radius and reaches a maximum.

gr-qc↗

arXiv2003

Interacting Geodesics: Binary Systems around a Black Hole

We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. We apply the technique in the of study two and three self-gravitating particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and noted differences in the structural stability, e.g., binary systems were found only in the general relativistic approach.

astro-ph↗

arXiv2002

Potential flows in a core-dipole-shell system: numerical results

Numerical solutions for: the integral curves of the velocity field (streamlines), the density contours, and the accretion rate of a steady-state flow of an ideal fluid with p=K n^(gamma) equation of state orbiting in a core-dipole-shell system are presented. For 1 < gamma < 2, we found that the non-linear contribution appearing in the partial differential equation for the velocity potential has little effect in the form of the streamlines and density contour lines, but can be noticed in the density values. The study of several cases indicates that this appears to be the general situation. The accretion rate was found to increase when the constant gamma decreases.

gr-qc↗

arXiv2002

Relativistic Multipoles and the Advance of the Perihelia

In order to shed some light in the meaning of the relativistic multipolar expansions we consider different static solutions of the axially symmetric vacuum Einstein equations that in the non relativistic limit have same Newtonian moments. The motion of test particles orbiting around different deformed attraction centers with the same Newtonian limit is studied paying special attention to the advance of the perihelion. We find discrepancies in the fourth order of the dimensionless parameter (mass of the attraction center)/(semilatus rectum). An evolution equation for the difference of the radial coordinate due to the use of different general relativistic multipole expansions is presented.

gr-qc↗

arXiv2001

Stability and chaos around multipolar deformed bodies: A general relativistic approach

The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test particles. For the prolate quadrupolar deformations we found chaotic motions contrary to the oblate case where only regular motion is found. We also study the metric that represents a rotating black hole deformed by a quadrupolar term. This metric is obtained as a two soliton solution in the context of Belinsky--Zakharov inverse scattering method. The stability of geodesics depends strongly on the relative direction of the spin of the center of attraction and the test particle angular momentum. The rotation does not alter the regularity of geodesic motions in the oblate case, i.e., the orbits in this case remain regular. We also employ the method of Lyapounov characteristic numbers to examine the stability of orbits evolving around deformed nonrotating centers of attraction. The typical time to observe instability of orbits is analyzed.

astro-ph↗

arXiv2001

Spacetime Defects: von Kármán vortex street like configurations

A special arrangement of spinning strings with dislocations similar to a von Kármán vortex street is studied. We numerically solve the geodesic equations for the special case of a test particle moving along twoinfinite rows of pure dislocations and also discuss the case of pure spinning defects.

gr-qc↗