Exact relativistic models of perfect fluid disks in a magnetic field

García-Reyes, Gonzalo; Espitia, Omar A.

doi:10.1007/s10714-014-1674-6

Cited by 5 publications

(11 citation statements)

References 40 publications

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“…Furthermore, when we take simultaneously k ω = 0 and β = 1, the results presented here describe the halo of the disks presented in [5] for the special case when the electric potential vanishes. The results presented here are compatibles wiht the results in the relativistic models of perfect fluid disks in a magnetic field presented in [8] and with the description of galactic halo presented in [4].…”

Section: Discussionsupporting

confidence: 90%

“…Our results are compatibles with the presented in [4] on possible features of galactic halo. Moreover, the description of the motion of charged particles on disk here deduced is in agreement with the results of analysis of particles motion in the magnetised disks discussed in [8]. As far as we know, this is the first relativistic model describing analytically the halo of a rotating source in presence of a magnetic field.…”

Section: Introductionsupporting

confidence: 87%

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Conformastationary disk-haloes in Einstein–Maxwell gravity

Gutiérrez-Piñeres

2015

Gen Relativ Gravit

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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. I. INTRODUCTORY REMARKSIn a recent work [1], we presented a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model was obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by using the distributional approach for the energy-momentum tensor. The class of solution corresponding to the model is asymptotically flat and singularity-free, and satisfies all the energy conditions. The purpose of the present work is to extend the above-mentioned study to the conformastationary case, and the Kuzmin solution of the Laplaces equation to include a "generalized" Kuzmin solution of the Laplace's equation. The reason to undertake such an endeavour are easy to understand. Indeed, the issue of the exact solution of the Einstein and Einstein-Maxwell equations describing isolated sources self gravitating in a stationary axially symmetric spacetime appears to be of great interest both from a mathematical and physical point of view. For details of the astrophysics importance and the most relevant developments concerning the disks and disk-haloes sources the reader is referred to the works [1, 2] and references therein.In this work we present a new exact solution of the Einstein-Maxwell field equations for a thin disk surrounded by a magnetized halo in a conformastationary background. This solution is notoriously simple in its mathematical form. Moreover, the interpretation of the energy-momentum tensor presented here generalises the commonly used pressure free models to a fluid with non-vanishing pressure, heat flux and anisotropic tensor. In Section II we present an exact general relativistic model describing a disk surrounded by an electromagnetized halo and we obtain a solution of the Einstein-Maxwell field equations in terms of a solution of Laplace's equation. In Section III we express the surface energy-momentum tensor of the disk in the canonical form and we present a physical interpretation of it in terms of a fluid with non-vanishing pressure and heat flux. In Section IV a particular family of conformastationary magnetized disk-haloes solutions is presented. We complete the paper with a discussion of the results in Section V. II. GENERAL RELATIVISTIC MAGNETIZED HALOES SURROUNDING THIN DISKSTo obtain an exact general relativistic model describing a disk surrounded by an electromagnetized halo in a conformastationary spacetime, we sol...

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Section: Discussionsupporting

confidence: 90%

Section: Introductionsupporting

confidence: 87%

Conformastationary disk-haloes in Einstein–Maxwell gravity

Gutiérrez-Piñeres

2015

Gen Relativ Gravit

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“…Our results are compatible with those presented in [53] on possible features of galactic halo. Moreover, the description of the motion of charged particles on disk is deduced and is in agreement with the results of the similar analysis discussed in [59]. As far as we know, this is the first relativistic model describing analytically the relativistic magnetized halo of a rotating disk.…”

Section: Introductory Remarkssupporting

confidence: 85%

Exact Relativistic Magnetized Haloes around Rotating Disks

Gutiérrez-Piñeres

Capistrano

2015

Advances in Mathematical Physics

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The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. 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. Introductory RemarksIn the observational context, many ambiguities still exist about the main constituents, geometry, and dynamics (thermodynamics) of the galactic disk-haloes. However, there are several different observations which probe the galactic and surrounding galactic magnetic field. For instance, it can be measured by nonthermal radio emission from energy equipartition that results from the interaction of magnetic energy with relativistic particles which can play a role in the formation of arms in spiral galaxies (see Krause's "Magnetic Fields and Halos in Spiral Galaxies" [1] and "Magnetic Fields in Spiral Galaxies" [2] and references therein). For nearby galaxies, other probes are used as optical polarization, polarized emission of clouds and dust grains, maser emissions, diffuse radio polarized emission, and rotation measures of background polarization sources also. Magnetic fields can be seen as a new structural quantity and added to other constituent parameters (e.g., -alpha lines, density mass, local shocks, etc.) are important to study the formation and dynamics of galaxies. Other works propose that magnetic fields also play important role in large-structure formation [3].It is important to stress that magnetic fields are found mainly in interstellar medium and can be found in every type of galaxies but remarkably noticed in spiral galaxies (see [4] and references therein). For instance, Milky Way has been actively studied in its three regions (central bulge, halo, and accretion disk). This motivates obtaining a proper description of magnetic fields from an oriented general principle and relativistic thin disks have been revealed as one of the best ways to study them. Relativistic disks were also extensively studied in literature in several configurations. Exact solutions that have relativistic static thin disks as their sources were first studied by Bonnor and Sackfield [5] and T. Morgan and L. Morgan [6,7]. Subsequently, several classes of exact solutions corresponding to static [8][9][10][11][12][13][14][15][16][17] and stationary [18][19][20][21][22] thin disks have been obtained by different authors.The superposition of a static or sta...

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“…This last expression was derived according to the discretization of the metric tensor (15) and all quantities are evaluated at z = 0 (see [27]).…”

Section: Introductionmentioning

confidence: 99%

General relativistic razor-thin disks with magnetically polarized matter

2018

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The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.

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Exact relativistic models of perfect fluid disks in a magnetic field

Cited by 5 publications

References 40 publications

Conformastationary disk-haloes in Einstein–Maxwell gravity

Conformastationary disk-haloes in Einstein–Maxwell gravity

Exact Relativistic Magnetized Haloes around Rotating Disks

General relativistic razor-thin disks with magnetically polarized matter

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