Anisotropic spheres with Van der Waals-type equation of state

We study static spherically symmetric space-time to describe relativistic compact objects with anisotropic matter distribution and derive two classes of exact models to the Einstein–Maxwell system with a modified Van der Waals equation of state. We motivate a Van der Waals-type equation of state to physically signify a high-density domain of quark matter, and the generated exact solutions are shown to contain several classes of exact models reported previously that correspond to various physical scenarios. Geometrical analysis shows that the physical quantities are well behaved so that these models may be used to describe anisotropic charged compact spheres.     

Absolute stability limit for relativistic charged spheres

We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.     

广义相对论中负指数多层球的结构及稳定性

本文运用广义相对论讨论了满足负指数多方状态方程的流体多层球。经典引力理论与相对论性理论的差别由σ标志。σ是球体中心处的压力与密度之比。通过数值积分得到了n<0的相对论性Emden函数。在-1ed^*也增大。 关键词：     

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρ _r ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ _x (or ρ _r ) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρ _r ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painlevé property. Further, it is observed that the solutions with NDG have no uncharged analogue.     

Schrödinger cat states and decoherence studies in cavity QED

We present exact, analytic and simple solutions of relativistic perfect fluid hydrodynamics. The solutions allow us to calculate the rapidity distribution of the particles produced at the freeze-out, and fit them to the measured rapidity distribution data. We also give an advanced estimation of the energy density reached in heavy ion collisions, and an improved estimation of the life-time of the reaction.     

A relativistic gravity train

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl’s theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.     

Gravitational Field of Gyratons

A gyraton is an object moving with the speed of light and having finite energy and internal angular momentum (spin). First, we derive the gravitational field of a gyraton in the linear approximation. After this we study solutions of the Einstein equations for gyratons. We demonstrate that these solutions in 4 and higher dimensions reduce to two linear problems in a Euclidean space. We obtain the exact solutions for relativistic gyratons, discuss their properties, and consider special examples.     

On relativistic models of strange stars

The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein’s field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.      

Relativistic non-instantaneous action-at-a-distance interactions

Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The Poincaré invariant parameters that label successive events along the world lines can be identified with the proper times of the particles provided that certain conditions are imposed on the interaction terms in the action. Further conditions on the interaction terms arise from the requirement that mass be a scalar. A generic class of theories with interactions that satisfy these conditions is found. The relativistic equations of motion for these theories are presented. We obtain exact circular orbits solutions of the relativistic one-body problem. The exact relativistic one-body Hamiltonian is also derived. The theory has three components: a linearly rising potential, a Coulomb-like interaction and a dynamical component to the Poincaré invariant mass. At the quantum level we obtain the generalized Klein–Gordon–Fock equation and the Dirac equation.     

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for static anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting caseμ,∝ r^-2 for the energy density which arises in many astrophysical applications. In the second class the singularity at the centre of the star is not present in the energy density.     

Generating Interior Sources for the Reissner-Nordström Metric

We study the Einstein-Maxwell equations for isotropic pressure distributions. We postulate a relationship between the electric field intensity and one of the gravitational potentials. An algorithm is developed that allows us to systematically generate new classes of exact solutions for charged relativistic stars. The solutions are expressed in terms of simple elementary functions; it is possible to parametrize the solutions so that different values of a constant allows us to tabulate the models. For a particular class it is possible to generate models without any integration. We study the qualitative features of a particular solution, and show that it is physically reasonable in the region of a spherical shell surrounding the centre.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.     

Gravitational decoupled charged anisotropic solutions in modified Gauss-Bonnet gravity

This paper is devoted to the study of charged anisotropic exact solutions for spherical geometry in the context of modified Gauss-Bonnet gravity using the gravitational decoupling technique. We take Krori-Barua solution in the presence of charge for a spherically symmetric self-gravitating system and extend it to obtain two anisotropic solutions through some constraints. We study the stability as well as the physical viability criterion of the resulting solutions using anisotropy, squared speed of sound parameter and energy bounds. Both models turn out to be physically viable and stable as they fulfill the required energy conditions and stability criterion. We conclude that the stability of both anisotropic solutions increases with a decrease in charge.     

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality.It is shown that,in addition to the conventional ones,a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems,namely,i) the statistical gauge invariance;ii) the dark components of the local observables;and iii)the fermion statistical blocking effects,based upon an asymptotic nonthermal ensemble,An application to models is presented to show the importance of the discussions.     

Compact anisotropic spheres with prescribed energy density

Abstract New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav. 21, 899–905 (1989)), and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav. 26, 75–84 (1994)), as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.     

The Lemaître-Schwarzschild Problem Revisited

The Lemaître and Schwarzschild analytical solutions for a relativistic spherical body of constant density are linked together through the use of the Weyl quadratic invariant. The critical radius for gravitational collapse of an incompressible fluid is shown to vary continuously from 9/8 of the Schwarzschild radius to the Schwarzschild radius itself while the internal pressures become locally anisotropic.     

Charged perfect fluids in the presence of a cosmological constant

We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.     

Exact Solutions of Einstein's Field Equations

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology 7, 37 (2001)] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration. On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the state of hydrostatic equilibrium in general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion given by Negi and Durgapal (2001), in fact, cannot meet the requirement of the‘actual mass’, set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution. This criterion provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity [that is, the state of hydrostatic equilibrium in general relativity]. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic star clusters with arbitrary large central redshifts. PACS :04.20.Jd; 04.40.Dg; 97.60.Jd.     

Relativistic Charged Star Solutions in Higher Dimensions

We present a class of relativistic solutions of the Einstein-Maxwell equations for a spherically symmetric charged static fluid sphere in higher dimensions. The interior space at t=constant considered here possess (D?1) dimensional spheroidal geometry described by a higher dimensional Vaidya-Tikekar metric. A class of new static solutions of coupled Einstein-Maxwell equations is obtained in a D-dimensional space-time by prescribing the geometry of a (D?1) dimensional hyper spheroid in hydrostatic equilibrium. The solutions of the Einstein-Maxwell field equations are employed to obtain relativistic models for charged compact stars with a suitable law for variation of electric field in terms of the charged fluid content in the interior of the sphere. The central density is found to depend on the space-time dimensions and a physically realistic model is permitted for (D≥4). The validity of both Strong Energy Condition (SEC), Weak Energy Condition (WEC) are studied for a given configuration and compactness of compact objects. We found new class of solutions with interesting stellar models where it permits a star with a core having different property than the rest which however disappears in higher dimensions. The effect of dimensions on the Electric charge of the compact object is studied. We note that the upper limit of the electric field is determined by the space-time dimensions which are determined.     

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.