In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane--Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the isothermal and non--isothermal regimes. For completeness, the Tolman mass is computed and analysed to some extend. As a complementary study we consider the impact of the Karmarkar condition on the mass and the Tolman mass functions respectively. Comparison with other results in literature are discussed.
A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the tangential pressures of the fluid. Doing so the generalized Lane--Emden equations are obtained and solved. Some specific models are obtained, and their physical properties are discussed.
An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. Again the formalism requires the knowledge of only one function (instead of two) to generate all possible solutions. To illustrate the method some known cases are recovered.
This paper examines the general formalism and applications of isotropic as well as anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical and Schwarzschild spacetimes in the interior and exterior regions, respectively. We use two polytropic equations of state to obtain physically viable solutions of the field equations. The hydrostatic equilibrium and Lane-Emden equations are developed for both isotropic as well as anisotropic cases. We study the effects of anisotropic pressure on the stellar structure. Moreover, we graphically inspect …
In this paper, we study the electromagnetic effects on stability of spherically symmetric anisotropic fluid distribution satisfying two polytropic equations of state and construct the corresponding generalized Tolman Oppenheimer Volkoff equations. We apply perturbations on matter variables via polytropic constant as well as polytropic index and formulate the force distribution function. It is found that the compact object is stable for feasible choice of perturbed polytropic index in the presence of charge.
This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $P=κρ^γ+αρ-β$ for a heuristic anisotropy. We integrated the corresponding Lane-Emden equation for several hundred models and found the parameter-space portion ensuring the configurations' acceptability. Polytrope based on the total energy density are more stable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tang…
A general formalism developed few years ago to model polytropic Newtonian stars with anisotropic pressure is applied to model stars for which, both, radial and tangential pressure satisfy polytropic equations of state. We obtain the corresponding Lane--Emden equation, and integrate it for a wide range of values of the parameters, thereby illustrating the effects of the pressure anisotropy on stellar objects. We calculate Chandrasekhar mass for a white dwarf and compare it with previous results. Finally, prospective applications to some astrophysical scenarios are discussed.
In this work we will analyse the complexity factor, proposed by L. Herrera, for spherically symmetric static matter distributions satisfying a polytropic equation through the gravitational decoupling method. Specifically, we will use the 2-step GD, which is a particular case of the extended geometric deformation (EGD), to obtain analytic polytropic solutions of Einstein's equations. In order to give an example, we construct a model satisfying a polytropic equation of state using Tolman IV as a seed solution.
This paper analyzes the anisotropic stellar evolution governed by a polytropic equation of state in the framework of $f(R,T,Q)$ gravity, where $Q=R_{ab}T^{ab}$. We construct the field equations, hydrostatic equilibrium equation and trace equation to obtain their solutions numerically under the influence of $σR^{2}+γQ$ gravity model, where $σ$ and $γ$ are arbitrary constants. We examine the dependence of various physical characteristics such as radial/tangential pressure, energy density, anisotropic factor, total mass and surface redshift for specific values of the model parameters. The physica…
In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of the fact that Gravitational Decoupling allows to decrease the number of degrees of freedom once a well known solution of the Einstein field equations is provided as a seed so after demanding the polytropic equation for the radial pressure the system is automatically closed. The approach not only allows to extend both isotropic or anisotropic known solutions but simplifies the computation of the Tolman mass whenever the Minimal Geometric Deformation is con…
We set up in detail the general formalism to model polytropic general relativistic stars with anisotropic pressure. We shall consider two different possible polytropic equations, all of which yield the same Lane-Emden equation in the Newtonian limit. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In this context, the Tolman mass, which is a measure of the active gravitational mass, is invoked to explain some features of the models.…
We present a detailed analysis of a general relativistic static spherical symmetric distribution in which both the radial and tangential pressures follow a master polytropic equation of state that generalizes the standard treatment and avoids the appearance of singularities in the system. In particular, we find the corresponding Lane-Emden equation and integrate it for a wide range of values of the parameters involved. We explore the parameter space with the aim to find the set of parameters leading to reasonable physical solutions. Also, we considered the effect of spherically symmetric pertu…
We discuss the effect that small fluctuations of local anisotropy of pressure, and energy density, may have on the occurrence of cracking in spherical compact objects, satisfying a polytropic equation of state. Two different kind of polytropes are considered. For both, it is shown that departures from equilibrium may lead to the appearance of cracking, for a wide range of values of the parameters defining the polytrope. Prospective applications of the obtained results, to some astrophysical scenarios, are pointed out.
We analyze in detail conformally flat spherically symmetric fluid distributions, satisfying a polytropic equation of state. Among the two possible families of relativistic polytropes, only one contains models which satisfy all the required physical conditions. The ensuing configurations are necessarily anisotropic and show interesting physical properties. Prospective applications of the presented models to the study of super-Chandrasekhar white dwarfs, are discussed.
The main theme of this work is the development of complexity induced generalized frameworks for static cylindrical polytropes. We consider two different definitions of generalized polytopes with charged anisotropic inner fluid distribution. A new methodology based on complexity factor for the generation of consistent sets of differential equations will be presented. We conclude our work by carrying out graphical analysis of developed frameworks.
We set up the general formalism to model polytropic Newtonian stars with anisotropic pressure. We obtain the corresponding Lane-Emden equation. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In particular, we calculate the Chandrasekhar mass for a white dwarf. It is clearly displayed how the Chandrasekhar mass limit changes depending on the anisotropy. Prospective astrophysical applications of the proposed approach are discussed.
In this paper, we study a family of two-component anisotropic polytropes which model a wide range of spherically symmetric astrophysical systems such as early-type baryonic galaxies. This family is found to contain a large class of models such as the hypervirial family (which satisfy the virial theorem locally), the Plummer and Hernquist models and Navarro-Frenk-White (NFW)-like models. The potential--density pair for these models are derived, as well as their velocity dispersions and anisotropy parameters. The projected quantities are computed and found to reduce to analytical expressions in …
Spherically symmetric relativistic stars with the polytropic equation of state (EoS), which possess the local pressure anisotropy, are considered within the framework of general relativity. The generalized Lane-Emden equations are derived for the arbitrary anisotropy parameter $Δ=p_t-p_r$ ($p_t$ and $p_r$ being the transverse and radial pressure, respectively). They are then applied to some special ansatz for the anisotropy parameter in the form of the differential relation between the anisotropy parameter $Δ$ and the metric function $ν$. The analytical solutions of the obtained equations are …
Dark matter halos modeled by polytropic spheres influenced by the relict cosmological constant and trapping polytropes forming supermassive black holes
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV) equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behaviour of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.
In this work we evaluate the physical acceptability of relativistic anisotropic spheres modeled by two polytropic equations of state -- with the same newtonian limit -- commonly used to describe compact objects in General Relativity. We integrate numerically the corresponding Lane-Emden equation in order to get density, mass and pressure profiles. An ansatz is used for the anisotropic pressure allowing us to have material configurations slightly deviated from isotropic condition. Numerical models are classified in a parameter space according to the number of physical acceptability conditions t…
We present a generalized piecewise polytropic parameterization for the neutron-star equation of state using an ansatz that imposes continuity in not only pressure and energy density, but also in the speed of sound. The universe of candidate equations of state is shown to admit preferred dividing densities, determined by minimizing an error norm consisting of integral astrophysical observables. Generalized piecewise polytropes accurately reproduce astrophysical observables, such as mass, radius, tidal deformability and mode frequencies, as well as thermodynamic quantities, such as the adiabatic…
A family of exact relativistic stellar models is described. The family generalizes Buchdahl's n=1 polytropic solution. The matter content is a perfect fluid and, excluding Buchdahl's original model, it behaves as a liquid at low pressures in the sense that the energy density is non-zero in the zero pressure limit. The equation of state has two free parameters, a scaling and a stiffness parameter. Depending on the value of the stiffness parameter the fluid behaviour can be divided in four different types. Physical quantities such as masses, radii and surface redshifts as well as density and pre…
This paper is an investigation of the stability of some ideal stars. It is in- tended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields and Black Holes. The work is based on an action principle for the complete system of metric and matter fields. We propose a complete revision of the treatment of boundary conditions. An ideal star in our terminology has spherical symmetry and an isentropic equation of state. In our first work on this subject it was assumed that the density vanishes beyond a …
We sketch an algorithm to generate exact anisotropic solutions starting from a barotropic EoS and setting an ansatz on the metric functions. To illustrate the method, we use a generalization of the polytropic equation of state consisting of a combination of a polytrope plus a linear term. Based on this generalization, we develop two models which are not deprived of physical meaning as well as fulfilling the stringent criteria of physical acceptability conditions. We also show that some relativistic anisotropic polytropic models may have singular tangential sound velocity for polytropic indexes…
We develop a thermodynamical model of fermionic dark matter halos at finite temperature. Statistical equilibrium states may be justified by a process of violent collisionless relaxation in the sense of Lynden-Bell or from a collisional relaxation of nongravitational origin if the fermions are self-interacting. The most probable state (maximum entropy state) generically has a "core-halo" structure with a quantum core (fermion ball) surrounded by an isothermal atmosphere. The quantum core is equivalent to a polytrope of index $n=3/2$. The Pauli exclusion principle creates a quantum pressure that…
This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter…
We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u^a and x^a. These conditions for timelike and spacelike conformal Ricci and conformal matter collineations for anisotropic fluid reduce to the conditions of perfect fluid when the heat flux and the traceless anisotropic stress tensor vanish. Further, for $α=0$ (the conformal …
The present work is an attempt to find possible traversable wormhole solutions in static spherically symmetric space-time supported by anisotropic matter field. Part of the work could be considered as a generalization of the work in Phys. Lett. B 757 (2016), 130 in the sense that it extends the work done therein. The paper provides several examples of wormholes in anisotropic pressure and provides general mechanisms for finding them. Finally the work examines the energy conditions corresponding to suggested wormhole solutions.
We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter. Three classes of new exact solutions are found to the Einstein-Maxwell system. This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity. We can regain anisotropic and isotropic models from our general class of solution. A physical analysis indicates that the charged solutions descr…
We study the geometry of a wormhole spacetime filled with anisotropic matter in the context of general relativity. In the course of the study, new static and spherically symmetric solutions, analytic and numerical ones, are found. We specify the existence condition for a wormhole throat. We analyze properties of the solutions after categorizing them based on the spacetime regularity and the signature of energy density. The necessary conditions which allow a wormhole spacetime to be nonsingular are described.
Solution of Einstein Field Equations for Anisotropic Matter with Vanishing Complexity: Spacetime Metric Satisfying Karmarkar Condition and Conformally Flat Geometry
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exis…
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.
A certain type of matter with anisotropic pressures can add to the Reissner-Nordström metric a term proportional to a power of the radial coordinate. Using the standard method of separating variables for the Hamilton-Jacobi equation, we study the shadow of the corresponding rotating solution, obtained through the Newman-Janis algorithm. We define and calculate three observables in order to characterize the position, size and shape of the shadow.
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…
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…
We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter distribution satisfies a linear equation of state consistent with quark matter. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The first class has a constant potential and is regular in the stellar interior. It contains the familiar Einstein model as a limiting case and we can generate finite masses for the star. The second class has a variable potential and singularity at the centre. A graphical …
We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's field equations, we choose the scale factor as a hyperbolic function, specifically, $a\left( t\right) =\sinh ^{\frac{1}{n}}\left( γt\right) $, where $γ$ and $n>0$ are arbitrary constants, which gives us a time-dependent deceleration parameter. Then we study our cosmological model under the conditions of the parameters as: $γ$ fixed and $n>1$. Our cosmologic…
We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our analysis covers matter models as different from each other as, e.g., collisionless matter, elastic matter and magnetic fields. The main result we prove is the existence of an `anisotropy classification' for the asymptotic behaviour of Bianchi type I cosmologies. The type of asymptotic behaviour of generic solutions is determined by one single parameter that desc…
It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions [WEC or NEC]). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term $Λ$ to be space variable, viz., $Λ= Λ(r)$. The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy condit…
We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers-Geroch transform are discussed. Example spacetimes that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the spacetimes with the appropriate matter distribution. Use of the transform with a black string seed is discussed.
The possibility of strange stars mixed with dark energy to be one of the candidates for dark energy stars is the main issue of the present study. Our investigation shows that quark matter acts as dark energy after a certain yet unknown critical condition inside the quark stars. Our proposed model reveals that strange stars mixed with dark energy feature a physically acceptable stable model mimic characteristics of dark energy stars. The plausible connections are shown through the mass-radius relation as well as the entropy and temperature. We particularly note that a two-fluid distribution is …
In this paper, we study the physical characteristics of anisotropic spherically symmetric quark star candidates for $R+2σT$ gravity model, where $R$, $σ$ and $T$ depict scalar curvature, coupling parameter, and the trace of the energy-momentum tensor, respectively. In order to analyze the structure formation of quark stars, we consider the Heintzmann solution and assume that strange quark matter is characterized by MIT bag model equation of state. We evaluate the unknown parameters through matching conditions and obtain the values of radii of strange quark stars using modified Tolman-Oppenheim…
This paper studies generalized Ellis-Bronikov (E-B) traversable wormholes in $f(R)$ extended gravity. We assume that these wormholes are supported by anisotropic dark matter (DM) according to the most often used phenomenological models, namely those of Navarro-Frenk-White (NFW), Thomas-Fermi (T-F), and Pseudo-isothermal (PI). Initially, we obtain the field equations in a general scenario of $f(R)$ theories in the metric formalism for the static and spherically symmetric Morris-Thorne spacetime. Then we particularize to a $f(R)$ model with power-law, including the Starobinky modified gravity. F…
The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically f(R,$\mathcal{T}$) gravity theory. Additionally, we have taken f(R,$\mathcal{T}$) as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})$=$R+2χ\mathcal{T}$,where $χ$ is a dimensionless coupling parameter, and the Lagrangian matter $\mathcal{L}_m=-\frac{1}{3}\left(2p_{t}+p_{r}\right)$, to describe the complete set of field equations f…
We present novel analytical solutions for linear-order gravitational waves or tensor perturbations in a flat Friedmann-Robertson-Walker universe containing two perfect fluids, radiation and pressureless dust, and allowing for neutrino anisotropic stress. One of the results is applicable to any sub-horizon gravitational wave in such a universe. Another result is applicable to gravitational waves of primordial origin, for example produced during inflation, and works both before and after they cross the horizon. These results improve on analytical approximations previously set out in the literatu…
Recently introduced exact solution of the Einstein gravity coupled minimally to an anisotropic fluid representing dark matter can well represent supermassive black holes in galactic nuclei with realistic distribution of dark matter around the black hole, given by the Hernquist-like density distribution. For these fluid-hairy black hole spacetimes, properties of the gravitational radiation, quasinormal ringing, and optical phenomena were studied, giving interesting results. Here, using the range of physical parameters of these spacetimes allowing for their relevance in astrophysics, we study th…
The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$ is a Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. To achieve the desired goal, we capitalized on the spherical symmetric space-time and utilized the embedding class-1 solution via Karmarkar's condition in modeling the matter profiles. To calculate the unidentified constraints, Schwarzschild exterior solution along with experimental statistics …
A new cosmological solution of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and with perfect fluid as matter sources is presented. The matter is described by a scalar field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario, in the first case universe evolves from singularity and in the second case universe expands without singularity.
