A rotating three component perfect fluid source and its junction with empty space-time

The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein’s equations. It is shown that these solutions are the familiar static perfect fluid cases commonly derived in curvature coordinates but now endowed with rotation. These are also shown to be potential fluid sources for not only Kerr but also Kerr-de Sitter empty space-time. The approach is further discussed in the context of T-solutions of Einstein’s equations and the vacuum T-solution outside a rotating source is presented. The interior source for these solutions is shown not to be a perfect fluid but rather an anisotropic three component perfect fluid for which the energy momentum tensor is derived. The Schwarzschild interior solution is given as an example of the approach.     

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.     

Non-minimally coupled dark fluid in Schwarzschild spacetime

If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid–gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in the presence of non-minimal coupling with a fluid, and find out the energy–density and pressure of the fluid. In the present case the perfect fluid is part of the solution of the modified Einstein equation. We also solve the modified Einstein equation, using the flat spacetime metric and show that in the presence of non-minimal coupling one can accommodate a perfect fluid of uniform energy–density and pressure in the flat spacetime. In both the cases the fluid pressure turns out to be negative. Except these non-trivial solutions it must be noted that the vacuum solutions also remain as trivial valid solutions of the modified Einstein equation in the presence of non-minimal coupling.     

On the hydrodynamics of steady black hole accretion

We study the stationary and axisymmetric flow of a perfect fluid accreted by a Kerr black hole. The equations for the flow lines are obtained. Explicit solutions are found in the case when the fluid has an equation of state pressure = energy density.Supported in part by CONACYT (Mexico).     

Perfect fluid metrics conformal to the Schwarzschild exterior spacetime

We construct perfect fluid spacetimes by performing a conformal transformation on a non-conformally flat vacuum solution, namely the Schwarzschild exterior metric. It should be noted that conformally Ricci flat perfect fluid solutions, except those that are conformally flat, are rarely reported explicitly. In this article it is demonstrated that perfect fluid metrics conformal to the Schwarzschild exterior line element are necessarily static. The Einstein field equations for the static case reduce to a fully determined system of three differential equations in three unknowns and the conformal factor is uniquely determined in closed form. The solution is analysed for physical plausibility by establishing the positivity of the energy density and pressure profiles graphically. Additionally, the solution is observed to be causal in an appropriate limit and both the energy density and pressure is shown to be decreasing outwards towards the boundary. Finally, the weak, strong and dominant energy conditions are found to be satisfied in the region under investigation. Accordingly, the most common elementary physical conditions are met and the model is seen to be suitable for a core-envelope stellar model.     

The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity

The work of a previous article [1] is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times.     

Bianchi Type VI0 Cosmological Models with Perfect Fluid and Dark Energy

We consider a self-consistent system of Bianchi Type VI₀ cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=??? with ????[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein??s field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in detail.     

Anisotropic fluid spheres in general relativity

A procedure is developed to find static solutions for anisotropic fluid spheres from known static solutions for perfect fluid spheres. The method is used to obtain four exact analytical solutions of Einstein’s equations for spherically symmetric self-gravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric. The physical features of one of the solutions are briefly discussed. Many previously known perfect fluid solutions are derived as particular cases.     

Higher Dimensional Bianchi Type-V Cosmological Models with Perfect Fluid and Dark Energy

We have studied the Bianchi type-V cosmological models with binary mixture of perfect fluid and dark energy in five dimensions. The perfect fluid is obeying the equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or the Chaplygin gas. The exact solutions of the Einstein’s field equations are obtained in quadrature form.     

Bianchi -V Space -Time with Anisotropic Dark Energy in General Relativity

In a spatially homogeneous and anisotropic Bianchi type-V space-time the consequences of the presence of dynamically anisotropic dark energy and perfect fluid with heat-conduction are studied. We assume that dark energy is minimally interacting with matter and has an equation of state which is modified in a consistent way with the conservation of energy momentum tensor. Exact solutions of Einstein field equations are obtained by taking constant value of deceleration parameter. We find that this assumption is reasonable for the observation of the present day universe. The physical and geometrical properties of the models, the behavior of the anisotropy of dark energy and the thermodynamical relations that govern such solutions are discussed in detail.     

Kerr–Newman-AdS black hole surrounded by perfect fluid matter in Rastall gravity

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to \(T^{\mu \nu }_{~~;\mu }=\lambda R^{,\nu }\). In this work, we derive the Kerr–Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman–Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy (\(\omega =-\,2/3\)) and the perfect fluid dark matter (\(\omega =-\,1/3\)). Firstly, the Rastall parameter \(\kappa \lambda \) could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity \(\alpha \), which depends on the black hole mass M and the Rastall parameter \(\kappa \lambda \). Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.     

Energy Conditions,Cosmological Solutions and Cosmic No-Hair Conjecture in Gauss-Bonnet Theory

A detailed investigation of Gauss-Bonnet theory has been done from a different perspective. At first, the standard energy conditions are discussed and modified forms have been presented. Then some cosmological solutions have been obtained in 5D for perfect fluid assuming that the extra dimensional metric coefficient decreases with time. For some particular choice of the parameters, exponential solutions are obtained and finally, Cosmic No-Hair Conjecture has been proved for Gauss-Bonnet dilatonic scalar coupled to Einstein gravity with coupling parameter growing linearly in time.     

Generalized Einstein static universe

We consider the equilibrium configurations for static spherically symmetric self-gravitating perfect fluids in general relativity. The fluid obeys an equation of state which is the extreme limit allowed by Hawking's strong energy condition. The new solutions we have found are generalized Einstein static universes which have a Killing horizon similar to the one we are familiar with from the vacuum Schwarzschild solution.     

Stationary and static axisymmetric perfect fluid solutions

Using a certain formalism for the stationary axisymmetric problem with source a rigidly rotating perfect fluid it is shown that under specific assumptions, covariantly imposed, the field equations are reduced to a system of two ordinary second order differential equations. Two known metrics are special solutions of this system. In addition two static axisymmetric perfect fluid solutions, with a spherically symmetric limit, are derived explicitly.     

Lie Groups of Conformal Motions Acting on Null Orbits

Space-times admitting a 3-dimensional Lie group of conformal motions acting on null orbits containing a 2-dimensional Abelian subgroup of isometries are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespective of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.     

2+1-dimensional gravitational decoupled anisotropic solutions

This paper investigates exact models for spherically symmetric anisotropic matter distribution in 2+1-dimensions via gravitational decoupling approach. For this purpose, we choose known spherical solutions with perfect fluid in the absence as well as the presence of cosmological constant and extend them to anisotropic models by imposing a constraint on matter components. The physical viability and stability of our developed solutions are investigated through graphical analysis of density, radial/tangential pressure, energy conditions, and causality criterion. It is found that both solutions are stable and satisfy all the physical requirements for the feasible choice of the model parameters.     

Homogeneous Bianchi type VI0 perfect fluid space-times

An algorithm is presented for generating new exact solutions of the Einstein equations for spatially homogeneous cosmological models of Bianchi type VI₀. The energy-momentum tensor is of perfect fluid type. Starting from Dunn and Tupper's dust-filled universe, new classes of solutions are obtained. The solutions represent anisotropic universes filled with perfect fluid not satisfying the equation of state. Some of their physical properties are studied.     

Power law singularities in orthogonal spatially homogeneous cosmologies

We investigate the structure of the so-called power asymptote singularities in orthogonal spatially homogeneous solutions of the Einstein field equations with perfect fluid source. We first give a systematic survey of the different possible power asymptotes, some of which are well known, and some new, and characterize them in a coordinate-independent manner. The known orthogonal spatially homogeneous exact solutions with perfect fluid source are then classified on the basis of which power asymptote they admit. In many cases this leads to simpler forms of the known solutions, and suggests methods for deriving new solutions.     

Nonminimally coupled scalar field and perfect fluid in Einstein–Cartan cosmology

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field and perfect fluid. Some effects of torsion are revealed by solving an analogous problem in general relativity. A comparative analysis of the cosmological models with and without perfect fluid is carried out in context of the Einstein–Cartan theory. The role of perfect fluid in the dynamics of models is discussed.     

Collapsing shear-free radiating fluid spheres

We present a new class of exact solutions of relativistic field equations for a collapsing spherically symmetric shear-free isotopic fluid undergoing radial heat flow. The interior solutions are matched with Vaidya exterior metric over the boundary. Initially the interior solutions represent a static configuration of perfect fluid which then gradually starts evolving into radiating collapse.