In this work, we present a class of relativistic and well-behaved solution to Einstein's field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different classes of new exact solution are found for anisotropy factor(delta). We have analyzed our model with various physical aspects such as pressure (radial as well as transverse), energy density, anisotropy factor, mass, compactness parameter, adiabatic index(gamma) and surface redshift. A graphical analysis of energy conditions, TOV equation and causality condition indicates the model are well behaved. The physical acceptability of the model has verified by considering compact objects with similar mass and radii, such as 4U 1820-30,Vela X-1, PSR J1614-2230, LMC X-4, SMC X-1, 4U 1538-52, Her X-1, Cyg X-2, PSR B1913+16 and PSR J1903+327.
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.
We compute the equilibrium, the fundamental eigenfrequency of oscillations modes, and quadrupolar tidal deformability of anisotropic polytropic spheres. These studies are respectively performed through the numerical solution of the Tolman-Oppenheimer-Volkoff equation, Chandrasekhar radial oscillation equations, and nonlinear first-order Riccati equation for tidal deformability, all modified from their original version to include the anisotropic effects. For the polytropic exponent $γ=2$ and the anisotropic model of Cattoen, Faber, and Visser, we show that the anisotropy could be reflected in t…
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…
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 this work we obtain an analytic and well behaved solution to Einstein's field equations describing anisotropic matter distribution. It's achieved in the embedding class one spacetime framework using Karmarkar's condition. We ansatz the metric potential $g_{tt}$ corresponding to Wyman IIa solution. The obtained model is representing some strange star candidates such as Cen X-3, LMC X-4 and 4U 1538-52. A graphical analysis shows that our model is free from physical and geometric singularities and satisfies all the physical admissibility conditions from the physical and mathematical point of v…
This paper is devoted to the formulation of a complexity factor for dynamical anisotropic sphere in the framework of $f(G,T)$ gravity, where $G$ is the Gauss-Bonnet invariant and $T$ is the trace of energy-momentum tensor. Inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms create complexity within the self-gravitating system. We evaluate the structure scalars by orthogonal splitting of the Riemann tensor to evaluate a complexity factor which incorporates all the fundamental properties of the system. Moreover, we examine the dynamics of the sphere by assumin…
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.
In the background of isotropic horizonless spheres, Hod recently provided an analytical proof of a bound on the compactness at the innermost light ring with the dominant energy and non-negative trace conditions. In this work, we extend the discussion of isotropic spheres to anisotropic spheres. With the same dominant energy and non-negative trace conditions, we prove that Hod's bound also holds in the case of anisotropic horizonless spheres.
Taking local anisotropy into consideration, in this paper, some new analytical models of relativistic anisotropic charged quark stars in linear and quadratic regime have been developed. The Einstein-Maxwell field equations have been solved with a particular form of metric potential and electric field intensity. The plots generated show that physical variables such as metric potentials, radial pressure, energy density, charge density, anisotropy, radial speed sound are consistent with realistic stellar models. We obtained some models consistent with stellar objects as 4U 1538-52, Cyg X-2, OGLE-…
We present a particular solution to the Einstein field equations that could arise as a magnetic monopole in the strong field limit of the Born-Infeld electrodynamics. We solve its geodesics exactly and show that they can mimic the gravitational lensing of a singular isothermal sphere, but with matter and radiation following the same trajectories. This solution has previously been called "cloud of strings" or "string hedgehog," and has appeared as the limit of a global O(3) monopole.
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise to a static radial electric field. The density of the fluid has the form $ρ(r) = ρ_o + αr^2$ (here $ρ_o$ and $α$ are constants) and the total charge $q(r)$ within a sphere of radius $r$ has the form $q = βr^3$ (with $β$ a constant). We evaluate the critical values of $M/R$ for these spheres as a function of $Q/R$ and compare these values with those given by …
In this paper, we develop two anisotropic solutions for static self-gravitating spherical structure in the presence of electromagnetic field through gravitational decoupling approach in $f(G,T)$ theory, where $G$ and $T$ denote the Gauss-Bonnet term and trace of the energy-momentum tensor, respectively. The extra source with isotropic seed sector is responsible for generating anisotropy in the spacetime. The system of field equations is decoupled into two arrays by using minimal geometric deformation in the radial component. The first set portrays the isotropic regime whereas the second set re…
This manuscript explores the compact geometries by employing Karmarkar condition with the charged anisotropic source of matter distribution. For this purpose, we consider an explicit model by indulging $\mathrm{g}_{rr}$ metric potential obeying the Karmarkar condition. Moreover, we ansatz the time metric co-efficient following the approach by Adler. The crucial aspect of present investigation is the implication of the Bardeen model as an outer spacetime. Implementation of Bardeen approach turns out to be very interesting as this corresponds to the magnetic mono-pole gravitational remnants emer…
We study the static stellar equilibrium configurations ofuncharged and charged spheres composed by a relativistic polytropic fluid, and compare with those of spheres composed by a non-relativistic polytropic fluid, the later case already being studied in a previous work [J. D. Arbañil, P. S. Lemos, V. T. Zanchin, Phys. Rev. D \textbf{88}, 084023 (2013)]. In the relativistic fluid case, a relativistic polytropic equation of state, $p=ωδ^γ$, is assumedd. Here, $δ=ρ-p/(γ-1)$, with $δ$ and $ρ$ being the rest mass density and the energy density, respectively, and $ω$ and $γ$ are respectively the po…
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 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…
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…
In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Hořava gravity and Einstein-aether theory. We assume a specific non-static configuration of the aether vector field and show that the field equations admit a family of exact analytical solutions which can be obtained if one of the two metric coefficients is assigned. We study as an illustrative example the case in which the metric of the interior spacetime reproduces the Newtonian potential of a fluid sphere with constant density.
