arXiv subjects

Patricio S. Letelier

Publications and source records attributed to Patricio S. Letelier.

At least 55 records · Page 3Linked to original sources

arXiv2001

On Accelerated Black Holes

The static and stationary C-metric are revisited in a generic framework and their interpretations studied in some detail. Specially those with two event horizons, one for the black hole and another for the acceleration. We found that: i) The spacetime of an accelerated static black hole is plagued by either conical singularities or lack of smoothness and compactness of the black hole horizon; ii) By using standard black hole thermodynamics we show that accelerated black holes have higher Hawking temperature than Unruh temperature of the accelerated frame; iii) The usual upper bound on the product of the mass and acceleration parameters <1/sqrt(27) is just a coordinate artifact. The main results are extended to accelerated rotating black holes with no significant changes.

gr-qc↗

arXiv2001

Acceleration, streamlines and potential flows in general relativity: analytical and numerical results

Analytical and numerical solutions for the integral curves of the velocity field (streamlines) of a steady-state flow of an ideal fluid with $p = ρ$ equation of state are presented. The streamlines associated with an accelerate black hole and a rigid sphere are studied in some detail, as well as, the velocity fields of a black hole and a rigid sphere in an external dipolar field (constant acceleration field). In the latter case the dipole field is produced by an axially symmetric halo or shell of matter. For each case the fluid density is studied using contour lines. We found that the presence of acceleration is detected by these contour lines. As far as we know this is the first time that the integral curves of the velocity field for accelerate objects and related spacetimes are studied in general relativity.

gr-qc↗

arXiv2000

Rotating Relativistic Thin Disks

Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to the geometric mean of the prograde and retrograde geodesic circular velocities of test particles moving on the disk. We also found that for generic disks we can have zones with heat flow. For the two families of models studied the boundaries that separate the zones with and without heat flow are not stable against radial perturbations (ring formation).

gr-qc↗

arXiv1999

Chaos and Fractals in Geodesic Motions Around a Non-Rotating Black-Hole with an External Halo

We investigate the occurrence chaos in the escape of test particles moving in the field of a Schwarzschild black hole surrounded by an external halo. The motion of both material particles and zero rest mass particles is considered. The chaos is characterized by the fractal dimension of boundary between the basins of the different escapes, which is a topologically invariant characterization. We find chaos in the motion of both material particles and null geodesics.

chao-dyn↗

arXiv1999

Fractal escapes in Newtonian and relativistic multipole gravitational fields

We study the planar motion of test particles in gravitational fields produced by an external material halo, of the type found in many astrophysical systems, such as elliptical galaxies and globular clusters. Both the Newtonian and the general-relativistic dynamics are examined, and in the relativistic case the dynamics of both massive and massless particles are investigated. The halo field is given in general by a multipole expansion; we restrict ourselves to multipole fields of pure order, whose Newtonian potentials are homogeneous polynomials in cartesian coordinates. A pure (n)-pole field has (n) different escapes, one of which is chosen by the particle according to its initial conditions. We find that the escape has a fractal dependency on the initial conditions for (n>2) both in the Newtonian and the relativistic cases for massive test particles, but with important differences between them. The relativistic motion of massless particles, however, was found to be regular for all the fields we could study. The box-counting dimension was used in each case to quantify the sensitivity to initial conditions which arises from the fractality of the escape route.

chao-dyn↗

arXiv1999

Scattering map for two black holes

We study the motion of light in the gravitational field of two Schwarzschild black holes, making the approximation that they are far apart, so that the motion of light rays in the neighborhood of one black hole can be considered to be the result of the action of each black hole separately. Using this approximation, the dynamics is reduced to a 2-dimensional map, which we study both numerically and analytically. The map is found to be chaotic, with a fractal basin boundary separating the possible outcomes of the orbits (escape or falling into one of the black holes). In the limit of large separation distances, the basin boundary becomes a self-similar Cantor set, and we find that the box-counting dimension decays slowly with the separation distance, following a logarithmic decay law.

gr-qc↗

arXiv1999

Exact General Relativistic Disks with Magnetic Fields

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bicak, Lynden-Bell and Katz [Phys. Rev. D47, 4334, 1993] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.

gr-qc↗

arXiv1998

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $γ$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.

gr-qc↗

arXiv1998

Relativistic and Newtonian core-shell models: analytical and numerical results

We make a detailed analysis of Newtonian as well as relativistic core-shell models recently proposed to describe a black hole or neutron star surrounded by shells of matter, and in a seminal sense also galaxies, supernovae and star remnants since there are massive shell-like structures surrounding many of them and also evidences for many galactic nuclei hiding black holes. We discuss the unicity of the models in relation to their analyticity at the black hole horizon and also to the full elimination of conical singularities. Secondly, we study the role played by the presence/lack of discrete reflection symmetries about equatorial planes in the chaotic behavior of the orbits, which is to be contrasted with the almost universal acceptance of reflection symmetries as default assumptions in galactic modeling. We also compare the related effects if we change a true central black hole by a Newtonian central mass. The numerical findings are: 1- The breakdown of the reflection symmetry about the equatorial plane in both Newtonian and relativistic core-shell models does i) enhance in a significant way the chaoticity of orbits in reflection symmetric oblate shell models and ii) inhibit significantly also the occurrence of chaos in reflection symmetric prolate shell models. In particular, in the prolate case the lack of the reflection symmetry provides the phase space with a robust family of regular orbits that is otherwise not found at higher energies. 2- The relative extents of the chaotic regions in the relativistic cases (i. e. with a true central black hole) are significantly larger than in the corresponding Newtonian ones (which have just a $-1/r$ central potential).

astro-ph↗

arXiv1997

Two Kerr black holes with axisymmetric spins: An improved Newtonian model for the head-on collision and gravitational radiation

We present a semi-analytical approach to the interaction of two (originally) Kerr black holes through a head-on collision process. An expression for the rate of emission of gravitational radiation is derived from an exact solution to the Einstein's field equations. The total amount of gravitational radiation emitted in the process is calculated and compared to current numerical investigations. We find that the spin-spin interaction increases the emission of gravitational wave energy up to 0.2% of the total rest mass. We discuss also the possibility of spin-exchange between the holes.

gr-qc↗

arXiv1997

On the integrability of halo dipoles in gravity

We stress that halo dipole components are nontrivial in core-halo systems in both Newton's gravity and General Relativity. To this end, we extend a recent exact relativistic model to include also a halo dipole component. Next, we consider orbits evolving in the inner vacuum between a monopolar core and a pure halo dipole and find that, while the Newtonian dynamics is integrable, its relativistic counterpart is chaotic. This shows that chaoticity due only to halo dipoles is an intrinsic relativistic gravitational effect.

gr-qc↗

arXiv1996

Curvature and Chaos in General Relativity

We clarify some points about the systems considered by Sota, Suzuki and Maeda in Class. Quantum Grav. 13, 1241 (1996). Contrary to the authors' claim for a non-homoclinic kind of chaos, we show the chaotic cases they considered are homoclinic in origin. The power of local criteria to predict chaos is once more questioned. We find that their local, curvature--based criterion is neither necessary nor sufficient for the occurrence of chaos. In fact, we argue that a merit of their search for local criteria applied to General Relativity is just to stress the weakness of locality itself, free of any pathologies related to the motion in effective Riemannian geometries.

gr-qc↗

arXiv1996

Addendum: Chaos around a Hénon-Heiles-Inspired Exact Perturbation of a Black Hole

We find that the model of a black hole plus an exterior halo of quadrupoles and octopoles recently proposed by us is more chaotic than previously detected. In fact, the quadrupolar component gives rise also to a chaotic behavior, found after further numerical search. This fact reinforces even more the role of chaos in relativistic core--halo models.

gr-qc↗

arXiv1996

Chaos around a Hénon-Heiles-inspired exact perturbation of a black hole

A solution of the Einstein's equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known Hénon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is studied and bounded zones of chaotic behavior are found.

gr-qc↗

arXiv1995

Loop Variables for a Class of Conical Spacetimes

Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string.

gr-qc↗

arXiv1995

Spacetime Defects: Torsion Loops

Spacetimes with everywhere vanishing curvature tensor, but with torsion different from zero only on world sheets that represent closed loops in ordinary space are presented, also defects along open curves with end points at infinity are studied. The case of defects along timelike loops is also considered and the geodesics in these spaces are briefly discussed.

gr-qc↗

arXiv1995

Bubbles and Wormholes: Analytic Models

The first junction conditions of spherically symmetric bubbles are solved for some cases, and whereby analytic models to the Einstein field equations are constructed. The effects of bubbles on the spacetime structure are studied and it is found that in some cases bubbles can close the spatial sector of the spacetime and turn it into a compact one, while in other cases they can give rise to wormholes. One of the most remarkable features of these wormholes is that they do not necessarily violate the weak and dominant energy condition even at the classical level.

gr-qc↗

arXiv1995

Dynamic wormholes and Energy Conditions

A class of exact solutions of the Einstein field equations representing non-static wormholes that obey the {\em weak and dominant energy conditions } is presented. Hence, in principle, these wormholes can be built with less exotic matter than the static ones.

gr-qc↗