arXiv subjects

Antonio C. Gutiérrez-Piñeres

Publications and source records attributed to Antonio C. Gutiérrez-Piñeres.

At least 19 recordsLinked to original sources

arXiv2026

Comment on ''The space-time line element for static ellipsoidal objects''

A recent paper proposes a static ellipsoidal space-time metric that reduces to Schwarzschild. After examining the corrected line element using Maple's Differential geometry package, we find that the Einstein tendor and Ricci scalar are non-zero, and the metric yields non-zero pressures when interpreted as an anisotropic fluid. Thus, it does not represent a vacuum solution. We also checked a cited ellipsoidal metric from the literature and found it likewise fails to satisfy the vacuum Einstein equations.

gr-qc↗

arXiv2024

$C^3$ matching conditions for anisotropic fluids

The $C^3$ approach is an invariant formalism that utilizes the eigenvalues of the Riemann curvature tensor to match spacetimes across a specific matching surface. We apply this approach to match an anisotropic fluid with an exterior vacuum solution, including the case in which discontinuities appear on the matching surface. As a particular example, a class of analytic solutions, which describe the gravitational field of realistic neutron stars, is matched to the exterior Schwarzschild spacetime.

gr-qc↗

arXiv2023

Fermi-normal coordinates for the Newtonian approximation of gravity

In this work, we compute the metric corresponding to a static and spherically symmetric mass distribution in the general relativistic weak field approximation to quadratic order in Fermi-normal coordinates surrounding a radial geodesic. To construct a geodesic and a convenient tetrad transported along it, we first introduce a general metric, use the Cartan formalism of differential forms, and then specialize the space-time by considering the nearly Newtonian metric. This procedure simplifies the calculations significantly, and the expression for the radial geodesic admits a simple form. We conclude that in quadratic order, the effects of a Schwarzschild gravitational field measured locally by a freely falling observer equals the measured by an observer in similar conditions in the presence of a Newtonian approximation of gravitation.

gr-qc↗

arXiv2019

$C^3$ matching for asymptotically flat spacetimes

We propose a criterion for finding the minimum distance at which an interior solution of Einstein's equations can be matched with an exterior asymptotically flat solution. It is based upon the analysis of the eigenvalues of the Riemann curvature tensor and their first derivatives, implying $C^3$ differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the $C^3$ matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.

gr-qc↗

arXiv2016

Effective perihelion advance and potentials in a conformastatic background with magnetic field

An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the Solar system and the Moon (EPM2011). We show that, in general, the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein gravity alone.

gr-qc↗

arXiv2016

On the thermal stability of a static spherically symmetric black holes in Nash embedding framework

We study the deformation caused by the influence of extrinsic curvature on a vacuum spherically symmetric metric embedded in a five-dimensional bulk. In this sense, we investigate the produced black-holes and derive general characteristics such as their masses, horizons, singularities and thermal properties. As a test, we also study the bending of light near such black-holes analyzing the movement of a test particle and the modification caused by extrinsic curvature on its movement. Accordingly, using the asymptotically conformal flat condition for the extrinsic curvature, an analytical expansion of a set of \emph{n}-scalar fields can be defined and we show that the corresponding black holes must be large and constrained in the range of allowed values $-1/2 \leq n \leq 1.8$. As a result, they are locally thermodynamically stable, but not globally preferred.

gr-qc↗

arXiv2016

Newman-Janis Ansatz in conformastatic spacetimes

The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.

gr-qc↗

arXiv2016

Test particles in a magnetized conformastatic spacetime

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function, which generates a singularity-free and asymptotically flat spacetime that describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles and the corresponding explicit value in the case of a punctual magnetic mass. We show that the analytical expressions obtained from our analysis are sufficient for being confronted with observations in order to establish whether such objects can exist in nature.

gr-qc↗

arXiv2015

Motion of test particles in a magnetized conformastatic background

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is investigated in the background of a space-time characterized by this class of solutions. We focus on the study of circular stable and unstable orbits obtained by taking account particular harmonic functions defining the gravitational potential. We show that is possible to have repulsive force generated by the charge distribution of the source. As the space-time here considered is singularity free we conclude that this phenomena is not exclusive to the case of naked singularities. Additionally, we obtain an expression for the perihelion advance of the test particles in a general magnetized conformastatic space-time.

gr-qc↗

arXiv2015

Exact Relativistic Magnetized halos around Rotating Disks

The exact relativistic treatment of a rotating disk surrounded by a magnetized material halo is presented. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.

gr-qc↗

arXiv2015

Conformastationary disk-haloes in Einstein-Maxwell gravity

An exact solution of the Einstein-Maxwell field equations for a conformastationary metric with magnetized disk-haloes sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A "generalization" of the Kuzmin solution of the Laplace's equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.

gr-qc↗

arXiv2014

Conformastationary disk-haloes in Einstein-Maxwell gravity II. The physical interpretation of the halo

The relativistic treatment of galaxies modelled as a rotating disk surrounded by a magnetised material halo is considered. The galactic halo is modelled by a magnetised mass-energy distribution described by the energy-momentum tensor of a general fluid in canonical form. All the dynamics quantities characterising the physical of the halo are expressed in exact form in terms of an arbitrary solution of the Laplace's equation. By way of illustration, a "generalisation" of the Kuzmin solution of the Laplace's equation is used. The motion of a charged particle on the halo region is described. All the relevant quantities and the motion of the charged particle show a reasonable physical behaviour.

gr-qc↗

arXiv2013

Exact relativistic models of thin disks around static black holes in a magnetic field

The exact superposition of a central static black hole with surrounding thin disk in presence of a magnetic field is investigated. We consider two models of disk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and other finite based on the first Morgan-Morgan disk. We also analyze a simple model of active galactic nuclei consisting of black hole, a Kuzmin-Chazy-Curzon disk and two rods representing jets, in presence of magnetic field. To explain the stability of the disks we consider the matter of the disk made of two pressureless streams of counterrotating charged particles (counterrotating model) moving along electrogeodesic. Using the Rayleigh criterion we derivate for circular orbits the stability conditions of the particles of the streams. The influence of the magnetic field on the matter properties of the disk and on its stability are also analyzed.

gr-qc↗

arXiv2013

Relativistic disks with two charged perfect fluids components

A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.

gr-qc↗

arXiv2013

Conformastatic disk-haloes in Einstein-Maxwell gravity

We present a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model is obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by using the distributional approach for the energy-momentum tensor. A class of solutions is obtained in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. A particular solution is given that is asymptotically flat and singularity-free, and satisfies all the energy conditions.

gr-qc↗

arXiv2012

Exact solutions in metric $f(R)$-gravity for static axisymmetric spacetime

Axially symmetric static vacuum exact solution (ASSVES) in Weyl coordinates are studied in $f(R)$ theories of gravity. In particular, we obtain a general explicit expression for the dependence between $df(R)/dR$ and the $r$ and $z$ coordinates and then the corresponding explicit form of $f(R)$ is obtained. Next, we present in detail the explicit solution of the modified field equations corresponding to the Newtonian potential due to a punctual mass placed at the origin of coordinates and also the Schwarzschild solution to the modified field equations.

gr-qc↗

arXiv2011

An infinite family of magnetized Morgan-Morgan relativistic thin disks

Applying the Horský-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. The resulting expressions are simply written in terms of oblate spheroidal coordinates and the solutions represent fields due to magnetized static thin disk of finite extension. Now, although the solutions are not asymptotically flat, the masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. Furthermore, the magnetic field and the circular velocity show an acceptable physical behavior.

gr-qc↗

arXiv2011

Relativistic static magnetized finite thin disk: An infinite family of exact solutions

An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horský-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field and the circular velocity are evaluated explicitly. All the physical quantities obtained shown an acceptable

astro-ph.CO↗