arXiv subjects

Guillermo A. González

Publications and source records attributed to Guillermo A. González.

35 records · Page 2Linked to original sources

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↗

arXiv2011

Stability of equatorial circular geodesics in static axially symmetric spacetimes

A general study of the stability of equatorial circular orbits in static axially symmetric gravitating systems is presented. Important circular geodesics as the marginally stable orbit, the marginally bounded orbit and the photon orbit are analyzed. We found general expressions for the radius, specific energy, specific angular momentum and the radius of the marginally stable orbit, both for null and timelike circular geodesics. Solutions expressed in cylindrical coordinates, oblate spheroidal coordinates, and prolate spheroidal coordinates are considered. We show that all null circular orbits are unstable and that there are not marginally stable null geodesics, whereas that for timelike geodesics the orbits can be unbounded, bounded or circulars.

gr-qc↗

arXiv2010

A local characterisation for static charged black holes

We obtain a purely local characterisation that singles out the Majumdar-Papapetrou class, the near-horizon Bertotti-Robinson geometry and the Reissner-Nordström exterior solution, together with its plane and hyperbolic counterparts, among the static electrovacuum spacetimes. These five classes are found to form the whole set of static Einstein-Maxwell fields without sources and conformally flat space of orbits, this is, the conformastat electrovacuum spacetimes. The main part of the proof consists in showing that a functional relationship between the gravitational and electromagnetic potentials must always exist. The classification procedure provides also an improved characterisation of Majumdar-Papapetrou, by only requiring a conformally flat space of orbits with a vanishing Ricci scalar of the usual conveniently rescaled 3-metric. A simple global consideration allows us to state that the asymptotically flat subset of the Majumdar-Papapetrou class and the Reissner-Nordström exterior solution are the only asymptotically flat conformastat electrovacuum spacetimes.

gr-qc↗

arXiv2009

Axially Symmetric Post-Newtonian Stellar Systems

We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations of classical ones. By introducing in the field equations provided by the 1PN approximation a known distribution function (DF) corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained, which are solved using the Hunter method. The rotation curves of the 1PN-corrected models differs from the classical ones and, for the generalized Kalnajs discs, the 1PN corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models.

gr-qc↗

arXiv2009

Rotating relativistic thin disks as sources of charged and magnetized Kerr-NUT spacetimes

A family of models of counterrotating and rotating relativistic thin discs of infinite extension based on a charged and magnetized Kerr-NUT metric are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. The metric considered has as limiting cases a charged and magnetized Taub-NUT solution and the well known Kerr-Newman solutions. We show that for Kerr-Newman fields the eigenvalues of the energy-momentum tensor of the disc are for all the values of the parameters real quantities so that these discs do not present heat flow in any case, whereas for charged and magnetized Kerr-NUT and Taub-NUT fields we find always regions with heat flow. We also find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disc as the superposition of two counterrotating charged dust fluids. We show that, in general, it is not possible to take the two counterrotating fluids as circulating along electrogeodesics nor take the two counterrotating tangential velocities as equal and opposite.

gr-qc↗

arXiv2009

A family of relativistic charged thin disks with an inner edge

A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitely computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.

gr-qc↗

arXiv2009

Finite thin disc models of four galaxies in the Ursa Major cluster: NGC3877, NGC3917, NGC3949 and NGC4010

Finite thin disc models of four galaxies in the Ursa Major cluster are presented. The models are obtained by means of the Hunter method and the particular solutions are choosen in such a way that the circular velocities are adjusted very accurately to the observed rotation curves of some specific spiral galaxies. We present particular models for the four galaxies NGC3877, NGC3917, NGC3949 and NGC4010 with data taken from the recent paper by Verheijen & Sancici (2001). By integrating the corresponding surface mass densities, we obtain the total mass M of these four galaxies, all of them being of the order of 10^10 solar masses. These obtained values for M may be taken as a quite accurately estimative of the mass upper bound of these galaxies, since in the model was considered that all their mass was concentrated at the galactic disc. The models can be consider as a first approximation to the obtaining of quite realistic models of spiral galaxies

astro-ph.GA↗

arXiv2009

Finite Axisymmetric Charged Dust Disks Sources for Conformastatic Spacetimes

An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the electromagnetic potential and the metric potential in terms of a solution of the Laplace equation. We give solutions to the Einstein-Maxwell equations with disk sources of finite extension in which the charge density is proportional to the energy surface density. We apply the well-know "inverse" approach to the gravitational potential representing finite thin disks given by Gonzalez and Reina to generate conformastatic charged dust thin discs. Exact examples of conformastatic metrics with disk sources are worked out in full.

gr-qc↗

arXiv2009

Exact Static Axially Symmetric Thin Annular Dust Disks

A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. The solutions describe an infinite family of static axially symmetric thin annular dust disks. The disk are of infinite extension but with an inner annular edge. The energy densities of the disks are everywhere positive functions of the radial coordinate, equals to zero at the inner edge of the disk, having a maximun at a finite value of the radius and then vanishing at infinity. The disks have finite mass and their energy-momentum tensor agrees with all the energy conditions.

gr-qc↗

arXiv2008

Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions

An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. Furthermore, the solutions are asymptotically flat and regular everywhere, as it is shown by computing all the curvature scalars. These solutions describe an infinite family of thin dust disks with a central inner edge, whose energy densities are everywhere positive and well behaved, in such a way that their energy-momentum tensor are in fully agreement with all the energy conditions. Now, although the disks are of infinite extension, all of them have finite mass. The superposition of the first member of this family with a Schwarzschild black hole was presented previously [G. A. González and A. C. Gutiérrez-Piñeres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent paper a detailed analysis of the corresponding superposition for the full family will be presented.

gr-qc↗

arXiv2008

Counterrotating Dust Disk Around a Schwarzschild Black Hole: New Fully Integrated Explicit Exact Solution

The first fully integrated explicit exact solution of the Einstein field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite annular thin disk (a disk with an inner edge) around the Schwarszchild black hole. The mass of the disk is finite and the energy-momentum tensor agrees with all the energy conditions. Furthermore, the total mass of the disk when the black hole is present is less than the total mass of the disk alone. The solution can also be interpreted as describing a thin disk made of two counterrotanting dust fluids that are also in agreement with all the energy conditions. Additionally, as we will show shortly in a subsequent paper, the above solution is the first one of an infinite family of solutions.

gr-qc↗

arXiv2008

Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.

gr-qc↗

arXiv2008

Counterrotating perfect fluid discs as sources of electrovacuum static spacetimes

The interpretation of some electrovacuum spacetimes in terms of counterrotating perfect fluid discs is presented. The interpretation is mades by means of an "inverse problem" approach used to obtain disc sources of known static solutions of the Einstein-Maxwell equations. In order to do such interpretation, a detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin discs with nonzero radial pressure. Four simple families of models of counterrotating charged discs based on Chazy-Curzon-type, Zipoy-Voorhees-type, Bonnor-Sackfield-type, and charged and magnetized Darmois electrovacuum metrics are considered where we obtain some discs with a CRM well behaved.

gr-qc↗

arXiv2008

Charged perfect fluid disks as sources of Taub-NUT-type spacetimes

The interpretation of a family of electrovacuum stationary Taub-NUT-type fields in terms of finite charged perfect fluid disks is presented. The interpretation is mades by means of an "inverse problem" approach used to obtain disk sources of known solutions of the Einstein or Einstein-Maxwell equations. The diagonalization of the energy-momentum tensor of the disks is facilitated in this case by the fact that it can be written as an upper right triangular matrix. We find that the inclusion of electromagnetic fields changes significatively the different material properties of the disks and so we can obtain, for some values of the parameters, finite charged perfect fluid disks that are in agreement with all the energy conditions.

gr-qc↗

arXiv2008

Electrovacuum Static Counterrotating Relativistic Dust Disks

A detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin disks without radial pressure. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We also find explicit expressions for the energy densities, charge densities and velocities of the counterrotating fluids. We then show that this constraint can be satisfied if we take the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. Four simple families of models of counterrotating charged disks based on Chazy-Curzon-like, Zipoy-Voorhees-like, Bonnor-Sackfield-like and Kerr-like electrovacuum solutions are considered where we obtain some disks with a CRM well behaved. The models are constructed using the well-known ``displace, cut and reflect'' method extended to solutions of vacuum Einstein-Maxwell equations.

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↗