Exact Relativistic Magnetized Haloes around Rotating Disks

Abstract

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...

Test particles in a magnetized conformastatic spacetime

“…In the subclass of conformastatic fields, it is also possible to consider electric and magnetic fields simultaneously [8]; nevertheless, the physical interpretation of the solutions in this case is more involved. In reference [7], for instance, this kind of solutions has been interpreted in terms of magnetized halos around thin disks. As we will see below, the restriction to only the magnetic component of the four-potential allows us to describe the gravitational field of compact objects endowed with magnetic fields.…”

“…The magnetic and gravitational field of such objects can reach very high values. In a series of recent works [6][7][8], several classes of static and stationary axisymmetric exact solutions of the Einstein-Maxwell equations were derived, which can be interpreted as describing the gravitational and magnetic fields of static and rotating thin disks. Although these solutions satisfy the main theoretical conditions to be considered as physically meaningful, additional tests are necessary in order to establish their applicability in realistic scenarios.…”

General relativistic razor-thin disks with magnetically polarized matter

“…], using the magnetized Reissner-Nordstrom metric, thin disk solutions composed by perfect fluid and magnetic fields were constructed. Recently in [16], solutions for a conformastationary metric with magnetized disk-haloes sources and solutions of rotating disks in magnetized haloes [17], were analyzed.…”

Newman–Janis Ansatz in conformastatic spacetimes

“…We follow the original terminology introduced by Synge [30], according to which stationary spacetimes with a conformally flat space of orbits constitute the conformastationary spacetimes, and conformastatic spacetimes comprises the static subset. Several exact solutions belonging to this class have been derived in a series of recent works [31][32][33][34] which are interpreted as describing the gravitational and magnetic fields of static and rotating thin disks. In this work, we start from a general conformastatic metric from which a stationary metric is obtained whose main physical are also analyzed.…”