Relativistic disks with two charged perfect fluids components

We present a relativistic model describing a thin disk system composed of two fluids. The system is surrounded by a halo in the presence of a non-trivial electromagnetic field. We show that the model is compatible with the variational multi-fluid thermodynamics formalism, allowing us to determine all the thermodynamic variables associated with the matter content of the disk. The asymptotic behaviour of these quantities indicates that the single fluid interpretation should be abandoned in favour of a two-fluid model.

General Relativity and Gravitation, 2018

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.

Gravitation and Cosmology, 2012

The paper presents a variety of classes of interior solutions of the Einstein-Maxwell field equations for a static, spherically symmetric distribution of a charged fluid of well-behaved nature. They describe perfect fluid balls with positive finite central pressure and density; their ratio is less than one (c = 1), and the causality condition is obeyed at the center. The outmarch of pressure, density, pressuredensity ratio and the adiabatic speed of sound is a monotonic decrease, in a physically appealing manner. A certain class of these well-behaved solutions is studied extensively. For this class, the mass of the configuration is maximized. In particular, for a surface density ρ b = 2 × 10 14 g/cm 3 we obtain a star with a maximum mass of 3.47M , a radius of 15.21 km and the central redshift 1.014385.

The European Physical Journal C, 2015

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein-Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like

A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. This criterion is applied to the class II Szafron-Szekeres perfect fluid space-times solutions, giving a very simple characterization of those that describe such thermal evolutions. For all of them, the significant thermodynamic variables are explicitly obtained. Also, the specific condition is given under which the divergence-free perfect fluid energy tensors may be interpreted as an ideal gas.

The European Physical Journal C, 80(5): 371, 2020

In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential e 2λ(r) and an equation of state. Specifically, the so-called modified generalized Chap-lygin equation of state with ω = 1 and depending on two parameters, namely, A and B. These ingredients close the problem, at least mathematically. However, to check the feasibility of the model, a complete physical analysis has been performed. Thus, we analyze the obtained geometry and the main physical observables, such as the density ρ, the radial p r , and tangential p t pressures as well as the anisotropy factor . Besides, the stability of the system has been checked by means of the velocities of the pressure waves and the rel-ativistic adiabatic index. It is found that the configuration is stable in considering the adiabatic index criteria and is under hydrostatic balance. Finally, to mimic a realistic compact object, we have imposed the radius to be R = 9.5 [km]. With this information and taking different values of the parameter A the total mass of the object has been determined. The resulting numerical values for the principal variables of the model established that the structure could represent a quark (strange) star mixed with dark energy.

2014

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving Einstein-Maxwell field equations with the preferred form of one of the metric potentials, a suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for matter distribution obtained in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g. electrically charged bare strange stars). These models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated numerically that the maximum compactness and mass increase in the presence of electric field and anisotropic pressures. Based on the analytic model developed in this present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known potential strange star candidates like PSR

Classical and Quantum Gravity, 2012

A detailed analysis of the surface energy-momentum (SEMT) tensor of stationary axially symmetric relativistic thin discs with nonzero radial pressure is presented. The physical content of the SEMT is analysed and expressions for the velocity vector, energy density, principal stresses and heat flow are obtained. We also present the counter-rotating model interpretation for these discs by considering the SEMT as the superposition of two counter-rotating perfect fluids. We analyse the possibility of counter-rotation along geodesics as well as counter-rotation with equal and opposite tangential velocities, and explicit expressions for the velocities are obtained in both the cases. By assuming a given choice for the counter-rotating velocities, explicit expressions for the energy densities and pressures of the counter-rotating fluids are then obtained. Some simple thin disc models obtained from the Kerr solution are also presented.

Physical Review D, 2004

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.

The pressure isotropy equation of Einstein’s field equations in case of static spherically symmetric isotropic metric usually has been reduced to Riccati type differential equation [1, 2]. Here this differential equation has been solved exactly for six particular forms of one of the metric potentials to produce six new exact solutions in simple algebraic forms. The perfect fluid spheres corresponding to these solutions are found to be well-behaved and pass all the elementary tests of physical acceptability. A similar approach has been followed, as one of our previous work (Pant, N., et al. Astrophys. Space Sci. 340, 407–412 (2012). doi:10.1007/s10509-012-1068-8 [3] hereafter paper I), for the determination of maximum mass of the compact fluid sphere. The analytical equation of state for the matter distribution obtained by our models may be astrophysically significant for the description of relativistic stellar structure of neutron stars or self-bound strange (quark) stars.