An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the eigenvalues of this tensor and the energy-momentum tensor of the solutions are given explicitly. All have the ring singularity of Kerr's solution and in addition the solution one more singularity and some solutions of the family additional singularities.The solution matches to the extremal solution of Kerr on two surfaces, which are thin shells and for proper values of the parameters of the solution approximate oblate spheroids. One of these surfaces has positive surface density. The solutions of the family satisfy the matching conditions with the solution of Kerr on two pair of surfaces, which are again thin shells. The surface density of one pair of surfaces is given explicitly. Also for proper values of the parameters of the solutions the surfaces of the other pair approximate oblate spheroids.
Here we look at an application of the Hartle metric to describe a rotating version of the spherical string cloud/ global monopole solution. While rotating versions of this solution have previously been constructed via the Newman-Janis algorithm, that process does not preserve the equation of state. The Hartle method allows for preservation of equation of state, at least in the sense of a slowly rotating perturbative solution. In addition to the direct utility of generating equations which could be used to model a region of a rotating string cloud or similar system, this work shows that it is p…
The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial profile of the stress anisotropy can be considered to decide potentially stable/unstable regions. Finally, pontentially stable/unstable regions of two known models of relativistic star have been examined.
In this paper, we study the shadow produced by rotating black holes with charge in the presence of an anisotropic matter field. We obtain the apparent shape and the corresponding observables characterizing the size, oblateness, and deviation of the center, for different values of the parameters of the model. We compare the new results with those corresponding to the Kerr-Newmann spacetime and we also discuss the observational prospects in this case.
Rotating and non-linear magnetic-charged black hole with an anisotropic matter field
School of Physics Science and Technology, Xinjiang University（新疆大学物理科学与技术学院）；Faculty of Science, Kunming University of Science and Technology（昆明理工大学理学院）
A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These solutions are required to satisfy regularity and junction conditions so that they can be possibly used to represent rotating astrophysical objects. Mathematical and physical properties are analyzed. The spacetime two independent parameters are physically interpreted, and they are shown to define two different solution classes together with stating the latters' prop…
New rotation laws have been recently found for general-relativistic self-gravitating stationary fluids. It was not clear whether they apply to systems rotating with a constant linear velocity. In this paper we fill this gap. The answer is positive. That means, in particular, that these systems should exhibit the recently discovered general-relativistic weak-field effects within rotating tori: the dynamic anti-dragging and the deviation from the Keplerian motion induced by the fluid selfgravity.
Rotating and twisting locally rotationally symmetric imperfect fluids in general relativity admit a much larger set of solutions than the self-similar ones recently suggested in the literature. Explicit forms of the metrics are given and the self-similar sub-cases are discussed.
In this note we show that the Linet-Tian family of solutions of the vacuum Einstein equations with a cosmological constant are a restricted set of the solutions of the Einstein field equations for a rotating perfect fluid previously found by A. Krasiński.
Recently, a generalised solution for Einstein equations of a rotating compact body, surrounded by matter field was proposed, which is the Kerr-Newman spacetime with an anisotropic matter. The solution possesses an additional hair, along with the conventional mass, charge and spin, which arises from the negative radial pressure of the anisotropic matter. In this article we show that, this new class of black holes can act as a particle accelerator during the collision of two generic particles in its gravitational field in the ergo-region. The centre of mass energy of the particles shoots to arbi…
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations are then obtained in covariant form for the anisotropic case. These equations are used to obtain new exact solutions using direct resolution and reconstruction techniques. Finally, we show that three of the generating theorems known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{μν}$ the eigenvalues of the tensor $R_μ^ν$ and the energy-momentum tensor $T_{μν}$ of the solutions are given explicitly. All members of the family have the ring singularity of Kerr's solution and most of them one or two more singularities. The solutions can be matched to the solution of Kerr on three closed surfaces, which for proper values of the parameters of the solutions approximate oblate spheroids. All match…
In this paper we present an exact solution of Einstein's fields equations describing dark matter possessing dark energy with negative pressure and energy equation of state parameter having minus sign.
In this paper we have considered an anisotropic space-time model of the Universe in presence of Brans-Dicke (BD) scalar field $ϕ$, causal viscous fluid and barotropic fluid. We have shown that irrespective of fluid the causality theory provides late time acceleration of the Universe. If the deceleration occurs in radial direction and acceleration occurs in transverse direction then the anisotropic Universe will accelerate for a particular condition of the power law representation of the scale factors.
We examine charged slowly rotating perfect fluids in the presence of a cosmological constant. The asymptotic form of the vacuum solutions to the linearised Einstein-Maxwell field equations is found and the possibility of matching this vacuum to the slow rotating García metric is considered. We show that, contrary to the case of zero cosmological constant, this García metric can be matched to an asymptotically de Sitter vacuum in the slow rotation limit. We conclude the García metric may potentially be suitable for describing a charged isolated rotating body in a cosmological background.
We describe a spheroidal fluid shell between two Kerr vacuum regions which have opposite rotation parameters. The shell has a stiff equation of state and a heat flow vector related to the rotational Killing current. The shell description is useful in exploring the significance of counter-rotation in Kerr metric matches.
Within the framework of $f(R,T)$ theories of gravity, we investigate the hydrostatic equilibrium of anisotropic neutron stars with a physically relevant equation of state (EoS) for the radial pressure. In particular, we focus on the $f(R,T) = R+ 2βT$ model, where $β$ is a minimal coupling constant. In the slowly rotating approximation, we derive the modified TOV equations and the expression for the relativistic moment of inertia. The main properties of neutron stars, such as radius, mass and moment of inertia, are studied in detail. Our results revel that the main consequence of the $2βT$ term…
Recent general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids allow one to rederive, in the first post-Newtonian approximation, the well known geometric dragging of frames, and two new weak-field effects within rotating tori. These are the recently discovered anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. They can be applied to the study of the existence of the (post-)Newtonian limits of solutions and in investigations of inequalities relating parameters of rotati…
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. The resulting solutions are also 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…
This paper is devoted to study the Bianchi type III model in the presence of anisotropic fluid in f(R) gravity. Exponential and power-law volumetric expansions are used to obtain exact solutions of the field equations. We discuss the physical behavior of the solutions and anisotropy behavior of the fluid, the expansion parameter and the model in future evolution of the universe.
The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein--Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.
Some anisotropic Bianchi V dark energy models are investigated in a scale invariant theory of gravity. We consider two non interacting fluids such as dark energy and a bulk viscous fluid. Dark energy pressure is considered to be anisotropic in different spatial directions. A dynamically evolving pressure anisotropy is obtained from the models. The models favour phantom behaviour. It is observed that, in presence of dark energy, bulk viscosity has no appreciable affect on the cosmic dynamics.
Given an anisotropic fluid source, we determine in closed forms, upon solving the field equations of general relativity (GR) and teleparallel gravity (TEGR) coupled to a cosmological constant, cylindrically symmetric four-dimensional cosmological rotating wormholes, satisfying all local energy conditions, and cosmological rotating solutions with two axes of symmetry at finite proper distance. These solutions have the property that their angular velocity is proportional to the cosmological constant.
In this work a new family of black hole solutions in Lovelock gravity is discussed. These solutions describe anisotropic fluids which extend to the spatial infinity. Though far from the horizon their geometries approach some previously known black holes solutions the location of the horizons differ. Furthemore, although the masses of these solutions match the masses of those previously known black holes, their temperatures and entropies differ.
The present paper deals with quantization of perfect fluid anisotropic cosmological models. Bianchi type V and IX models are discussed following Schutz's method of expressing fluid velocities in terms of six potentials. The wave functions are found for several examples of equations of state. In one case a complete wave packet could be formed analytically. The initial singularity of a zero proper volume can be avoided in this case, but it is plagued by the usual problem of non-unitarity of anisotropic quantum cosmological models. It is seen that a particular operator ordering alleviates this pr…
The article is devoted to cosmology. It deals with homogeneous anisotropic cosmological models. Scale factors have been evaluated for the multicomponent models with perfect fluid, taking account of its expansion, rotation and shear. The cosmological fluid components are as follows: phantom matter, de Sitter vacuum, domain walls, strings, dust, radiation, perfect gas, stiff matter and ekpyrotic matter. The scale factor dependences on the equation of state and kinematic invariants of the perfect fluid have been analysed. The paper is aimed at finding exact solutions of Friedmann and Raychaudhuri…
In this paper, we have studied the new exact model of anisotropic star in $f(T)$ theory of gravity. The dynamical equations in $f(T)$ theory with the anisotropic fluid have been solved by using Krori-Barua solution. We have determined that all the obtained solutions are free from central singularity and potentially stable. The observed values of mass and radius of the different strange stars RX J 1856-37, Her X-1, and Vela X-12 have been used to calculate the values of unknown constants in Krori and Barua metric. The physical parameters like anisotropy, stability and redshift of the stars have…
In the present work, we discuss the Wheeler-DeWitt quantization scheme for an n-dimensional anisotropic cosmological model with a perfect fluid in presence of a massless scalar field. We identify the time parameter using the generalization of Schutz formalism and find the wavepacket of the universe following standard Wheeler-DeWitt methodology of quantum cosmology. We also calculate the expectation values of scale factors and volume element. We show that quantized model escapes the singularity and supports bouncing universe solutions.
In this paper we revisit and extend the prior work of Filho and Bezerra [Phys. Rev D, 64, 084009 (2001)] to rotating dyonic global monopoles in presence of a perfect fluid. We then show that the surface topology at the event horizon, related to the metric computed, is a 2- sphere using the Gauss-Bonnet theorem. By choosing $ω=-1/3, 0, 1/3$ we investigate the effect of dark matter, dust, radiation on the silhouette of black hole. The presence of the global monopole parameter $γ$ and the perfect fluid parameters $\upsilon$, also deforms the shape of black hole's shadow, which has been depicted t…
We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson's equation of Newtonian gravity and its corresponding circular speed profile. As simple examples, we present three families of spherically symmetric spacetimes which we apply in constructing new models of relativistic anisotropic thick spherical shells, and of relativistic galaxy models composite by a central spherical bulge, the thick disk and the dark matter halo, writing in this case the metric in cylindrical coordinates. Moreover, the geodesic m…
Cosmological solutions are obtained in an anisotropic Kantowski-Sachs (KS) and Bianchi Type-I universes considering a cosmological constant with Skyrme fluid. Interestingly, the solutions obtained here in both the KS and Bianchi-I anisotropic universes are found isotropize at late time due to the presence of the Skyrme fluid even in the absence of $Λ$ term or any inflationary mechanism involving the inflaton field. A comparative study of both the anisotropic cosmological models are carried out here and found that Bianchi-I universe admits oscillatory solutions for a given matter configuration.…
