Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Pulsating stars in general relativity

The equation governing radial pulsations of fully relativistic stars is derived and expressed in terms of quantities which are continuous even across density discontinuities which occur, e.g., in zero-temperature stellar models that undergo electron capture. When expressed in terms of these quantities, the pulsation equation can be integrated through density discontinuities without any special treatment of these points being necessary. Expressions for the adiabatic index and pulsation energy are derived in a simple way.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant 70-1866.     

The charged line-mass in general relativity

The two exterior solutions for a charged line-mass are examined. In both cases the mass per unit length is negative.     

Static charged dust in general relativity

Solutions of the Einstein-Maxwell equations for static charged dust are discussed. Contrary to what has been asserted earlier it is found that cylindrically symmetric and plane symmetric solutions with the following properties, exist: (a) They are regular in the interior region; (b) the mass density is positive and vanishes at the boundary; (c) the metric, its first derivate, and the electrical field strength are continuous at the boundary; (d) the solutions are mirror symmetric in the plane symmetric case.     

Generalised model for anisotropic compact stars

In the present investigation an exact generalised model for anisotropic compact stars of embedding class 1 is sought with a general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass–radius relation, stability of the models, in connection to their validity. It is observed that the model presented here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates RXJ 1856-37, SAX J 1808.4-3658 (SS1) and SAX J 1808.4-3658 (SS2) are concerned.     

Equilibrium of charged dust in general relativity

Equilibrium of charged dust is studied in both the classical and relativistic theories. It is already known that the configuration of the dust is arbitrary if the ratio of the charge to mass densities,/, is everywhere ± 1 (in relativistic units). I show here that there are equilibrium configurations for certain other values/, including nonuniform ones. The solutions in these cases are arbitrary up to the choice of a harmonic function and a function of the electrostatic potential. In general they contain singularities.     

Static charged gas spheres in general relativity

In the present paper the field equations of general relativity have been solved to obtain the different solutions for the static charged gas sphere. These solutions are free from singularities and satisfy the necessary physical conditions.     

Nonstatic charged fluid spheres in general relativity

Faulkes has shown that shear-free solutions of the Einstein-Maxwell field equations can be found by solving a single second-order nonlinear differential equation containing two arbitrary functions of the radial coordinate. In this work a very general method is proposed to solve this nonlinear equation which, in effect, extends an earlier work of Wyman to its electromagnetic analog.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

Conformally symmetric anisotropic magnetospheres in general relativity

A class of exact analytical solutions of Einstein-Maxwell equations is obtained for static spheres of Maugin's anisotropic magnetofluid where the space-time geometry is assumed to admit a nonstatic conformai symmetry. These solutions are found by utilizing special physical considerations.     

Geometry of rotating charged bubbles in general relativity

It is shown that the spatial geometry of the bubbles with a constant radial coordinater _o, embedded in the Kerr-Newman manifold, does not depend on the mass and charge of this solution when referred to a coordinate frame rigidly rotating with the angular velocity =a(r ₀ ^{2+a 2})^–1. The corresponding line element is found to be identical to the one obtained by Smarr for the surface geometry of a charged rotating black hole.     

Minimum size of charged particles in general relativity

Spherical charged matter distributions are examined in a coordinate-free manner within the framework of general relativity. Irrespective of models chosen to describe the interior structure of a charged particle, it is found that the latter's total gravitational mass is positive definite, being finite only when there exists a lower bound for its invariant extension. For a simple choice of matter and charge distributions it is then shown that there is a minimum invariant size for the particle, below which no solution of the field equations exists, the matter density becoming negative and the spacetime developing an intrinsic singularity in the exterior of the particle for radii less than this minimum. A mass renormalization is derived, valid at the moment of time symmetry, which relates the particle's total mass to its charge, bare mass and invariant extension. Our results are compared with those obtained previously by Arnowitt, Deser and Misner, who consider the simpler distribution of a charged spherical shell. Qualitatively, the two situations share the same features. However, in the more realistic spherical distributions the formulae are correspondingly more complicated, and the minimum extension is found to be greater than that of the shell, as one might expect on physical grounds. Moreover, the correspondence between negative valued matter distributions and intrinsic singularities was not evident in the shell case.     

Relativistic polytropic models of charged anisotropic compact objects

In this paper, we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity (\begin{document}${\rm GR}$\end{document}). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state (\begin{document}${\rm EoS}$\end{document}). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., \begin{document}$\eta= \dfrac{1}{2},~ \dfrac{2}{3},~ 1$\end{document}, and \begin{document}$ 2 $\end{document}. Next, numerous physical characteristics of these considered models were studied via graphical analysis, and they were found to obey all the essential conditions for astrophysical compact objects. Furthermore, such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear, quadratic, and polytropic \begin{document}${\rm EoS}$\end{document}     

New solutions for charged spheres in general relativity

Exact solutions of the Einstein-Maxwell field equations are obtained for the case of static and spherically symmetric distribution of charged matter. The solutions are obtained through the extension of a method originally used for neutral configurations and are conveniently matched to the Reissner-Nordstrom exterior metric. The physical plausability of the solutions is discussed and it is shown that some of them reduce in appropriate limits to known neutral or charged solutions.     

On the existence of rotating stars in general relativity

The Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit of Einstein's equations. For a sufficiently small constant the existence of a set of solutions (0) of Einstein's equations of a stationary, axisymmetric star is proven. This existence is proven in weighted Sobolev spaces with the implicit function theorem. Since the value of the causality constant depends only on the units used to measure the velocity, the existence of a solution for any small is physically interesting.     

Collapse of magnetized hypermassive neutron stars in general relativity

Hypermassive neutron stars (HMNSs)--equilibrium configurations supported against collapse by rapid differential rotation--are possible transient remnants of binary neutron-star mergers. Using newly developed codes for magnetohydrodynamic simulations in dynamical spacetimes, we are able to track the evolution of a magnetized HMNS in full general relativity for the first time. We find that secular angular momentum transport due to magnetic braking and the magnetorotational instability results in the collapse of an HMNS to a rotating black hole, accompanied by a gravitational wave burst. The nascent black hole is surrounded by a hot, massive torus undergoing quasistationary accretion and a collimated magnetic field. This scenario suggests that HMNS collapse is a possible candidate for the central engine of short gamma-ray bursts.     

The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.