Perfect Fluid Configurations Research Articles

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

Complexity-free charged anisotropic Finch-Skea model satisfying Karmarkar condition

By making use of the extended geometric deformation (EGD) approach, this work explores the charged anisotropic Finch-Skea solution satisfying the Karmarkar condition. The implementation of EGD-approach splits the original gravitational source into perfect and anisotropic fluid configurations. We employ Herrera’s complexity factor Herrera L (2018 Phys. Rev. D 97 044010) formalism to develop theoretical models characterizing the role of complexity in the Finch-Skea solution. The use of the Karmarkar condition enables us to derive a solution for the isotropic, charged spherical configuration by defining a Finch-Skea metric that evaluates the deformation functions. The Finch-Skea ansatz serves as a valuable seed model for solving the seed-gravitational source, however, the zero-complexity constraint is employed to solve the remaining set of anisotropic equations. We match the interior metric manifold attributed to the spherically symmetric ansatz with the classical Reissner-Nordström metric. We examined the influence of gravitational decoupling on the anisotropic Finch-Skea solution. We also analyzed the physical viability of the presented results using graphical representations for the thermodynamic variables.

Dragged surfaces. On the accretion tori in the ergoregion

Abstract We discuss the conditions for the existence of extended matter configurations orbiting in the ergoregion or close to the outer ergosurface of the Kerr black hole (“dragged” configurations). The co-rotating tori under consideration are perfect fluid configurations with barotropic equations of state, orbiting on the equatorial plane of the central Kerr black hole. The possibility of magnetized tori with a toroidal magnetic field is also discussed. Indications on the attractors where dragged tori can be observed are provided with the analysis of the fluid characteristics and geometrical features, relevant for the torus stability and their observations. QPO emissions from the inner edges of the dragged tori are also discussed. We argue that the smaller dragged tori could be subjected to a characteristic instability: the effect of the frame-dragging. This possibility is thoroughly explored. This can finally lead to the destruction of the torus (disk exfoliation) which can combine with accretion and processes present in the region very close to the black hole horizon. Tori are characterized according to the central attractor dimensionless spin. These structures can be observed in orbiting black holes with dimensionless spin a > 0.9897 M.

Gravastars in f(R,T,RμνTμν) gravity

This work is devoted to study the analytical and regular solutions of a particular self-gravitating object (i.e., gravastar) in a particular theory of gravity. We derive the corresponding field equations in the presence of effective energy momentum tensor associated with the perfect fluid configuration of a spherical system. We then describe the mathematical formulations of the three respective regions i.e., inner, shell and exterior of a gravastar separately. Additionally, the significance and physical characteristics along with the graphical representation of gravastars are discussed in detail. It is seen that under some specific constraints, $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity is likely to host gravastars.

Anisotropic neutron stars by gravitational decoupling

In this work we obtain an anisotropic neutron star solution by gravitational decoupling starting from a perfect fluid configuration which has been used to model the compact object PSR J0348+0432. Additionally, we consider the same solution to model the Binary Pulsar SAX J1808.4-3658 and X-ray Binaries Her X-1 and Cen X-3 ones. We study the acceptability conditions and obtain that the MGD-deformed solution obey the same physical requirements as its isotropic counterpart. Finally, we conclude that the most stable solutions, according to the adiabatic index and gravitational cracking criterion, are those with the smallest compactness parameters, namely SAX J1808.4-3658 and Her X-1.

New agegraphic dark energy in f(G, T) gravity

This paper is devoted to the reconstruction paradigm for new agegraphic dark energy model in the context of f(G, T) gravity (G and T denote the Gauss–Bonnet invariant and trace of the energy-momentum tensor). To accomplish this, we choose the correspondence scenario for pressureless perfect fluid configuration in the framework of flat FRW universe. The cosmic behavior of reconstructed models is analyzed through cosmic diagnostic parameters and phase planes. It is found that the deceleration parameter indicates accelerated regime while the equation of state parameter gives the phantom phase for non-conserved and quintessence universe for conserved energy-momentum tensor. The squared speed of sound parameter represents the stability of the conserved model for late-time cosmic evolutionary paradigm whereas instability for the non-conserved regime. The trajectories of ωeff−ωeff′ plane correspond to thawing as well as freezing region for the non-conserved and conserved scenario, respectively. The r−s plane gives phantom as well as the non-phantom regime for conserved and Chaplygin gas model for the non-conserved paradigm. We conclude that the resulting models exhibit self-consistent quintessence as well as the phantom-like universe for appropriate choice of free parameters.

Bounds on higher derivative f(R,□R,T) models from energy conditions

This paper studies the viable regions of some cosmic models in a higher derivative [Formula: see text] theory with the help of energy conditions (where [Formula: see text], [Formula: see text] and [Formula: see text] are the Ricci scalar, d’Alembert’s operator and trace of energy–momentum tensor, respectively). For this purpose, we assume a flat Friedmann–Lemaître–Robertson–Walker metric which is assumed to be filled with perfect fluid configurations. We take two distinct realistic models that might be helpful to explore stable regimes of cosmological solutions. After taking some numerical values of cosmic parameters, like crackle, snap, jerk (etc.) as well as viable constraints from energy conditions, the viable zones for the under observed [Formula: see text] models are examined.

A simple method to generate exact physically acceptable anisotropic solutions in general relativity

By using the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling), we show a simple and powerful method to generate physically acceptable exact analytical solutions for anisotropic stellar distributions in general relativity. We find that some perfect fluid configurations could be incompatible with anisotropic effects produced by scalar fields.

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.

General relativistic polytropes with a repulsive cosmological constant

Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters---the polytropic index $n$, the ratio of central pressure and central energy density of matter $\ensuremath{\sigma}$, and the ratio of energy density of vacuum and central density of matter $\ensuremath{\lambda}$. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with $n=0$ corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of $n>0$, the static equilibrium configurations with fixed parameters $n$, $\ensuremath{\sigma}$, are allowed only up to a critical value of the cosmological parameter ${\ensuremath{\lambda}}_{\mathrm{c}}={\ensuremath{\lambda}}_{\mathrm{c}}(n,\ensuremath{\sigma})$. In the case of $n>3$, the critical value ${\ensuremath{\lambda}}_{\mathrm{c}}$ tends to zero for special values of $\ensuremath{\sigma}$. The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension $\ensuremath{\ell}>100\text{ }\text{ }\mathrm{kpc}$ and mass $M>1{0}^{12}\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$. For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than $\ensuremath{\lambda}={\ensuremath{\rho}}_{\text{vac}}/{\ensuremath{\rho}}_{\mathrm{c}}\ensuremath{\sim}{10}^{\ensuremath{-}9}$. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea that the static radius represents a natural limit on the extension of gravitationally bound configurations in an expanding universe dominated by the vacuum energy.

Binding energy in self-gravitating charged plane symmetric systems

This paper explores gravitational binding energy in static charged planar spacetime with perfect fluid configuration. We use Darmois formalism to explore the matching conditions of planar symmetry as an interior region and charged Vaidya as an exterior. The mass function is evaluated over the hypersurface to investigate the binding energy in the interior region. We conclude that gravitational field of the planar spacetime binds only the localized part while the non-localized part is due to the electric coupling.

On the locally rotationally symmetric Einstein–Maxwell perfect fluid

We examine the stability of Einstein–Maxwell perfect fluid configurations with a privileged radial direction by means of a $$1+1+2$$ -tetrad formalism. We use this formalism to cast in a quasilinear symmetric hyperbolic form the equations describing the evolution of the system. This hyperbolic reduction is used to discuss the stability of linear perturbations in some special cases. By restricting the analysis to isotropic fluid configurations, we assume a constant electrical conductivity coefficient for the fluid. As a result of this analysis we provide a complete classification and characterization of various stable and unstable configurations. We find, in particular, that in many cases the stability conditions are strongly determined by the constitutive equations and the electric conductivity. A threshold for the emergence of the instability appears in both contracting and expanding systems.

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Pseudo-Newtonian gravitational potential introduced in spherically symmetric black-hole spacetimes with a repulsive cosmological constant is tested for equilibrium toroidal configurations of barotropic perfect fluid orbiting the black holes. Shapes and potential depths are determined for the marginally stable barotropic tori with uniform distribution of specific angular momentum, using both the pseudo-Newtonian and fully relativistic approach. For the adiabatic (isoentropic) perfect fluid, temperature profiles, mass-density and pressure profiles and total masses of pseudo-Newtonian and relativistic tori are compared providing important information on the relevance of the test-disc approximation in both the approaches. It is shown that the pseudo-Newtonian approach can be precise enough and useful for the modelling of accretion discs in the Schwarzschild–de Sitter spacetimes with the cosmological parameter y = ΛM2/3 ≲ 10−6. For astrophysically relevant black holes with y < 10−25, this statement is tested and shown to be precise in few per cent for both accretion and excretion tori and for the marginally bound, i.e. maximally extended, tori allowing simultaneous inflow to the black hole and outflow to the outer space.

Lagrangian perturbation theory for rotating magnetic stars

Motivated by the possibility of radiation driven instabilities in rotating magnetic stars, we study the stability properties of general linear perturbations of a stationary and axisymmetric, infinitely conducting perfect fluid configuration threaded by a magnetic field and surrounded by vacuum. We develop a Lagrangian perturbation framework which enables us to formulate a strict stability criterion based on the notion of a canonical energy (a functional of the fluid displacement $\xi $ and its first time derivative). For any given choice of $\{\xi,\partial_t \xi \} $, the sign of the canonical energy determines whether the configuration is stable or not at the linear level. Our analysis provides the first complete description of the stability problem for a magnetic star, allowing for both rotation and the presence of a magnetic field in the exterior vacuum region. A key feature of the Lagrangian formulation is the existence of so-called `trivial' fluid displacements, which do not represent true physical perturbations. In order for the stability criterion to make rigorous sense one has to isolate these trivials and consider only the physical `canonical' displacements. We discuss this problem and formulate a condition which must be satisfied by all canonical displacements. Having obtained a well-defined stability criterion we provide examples which indicate that the magnetic field has a stabilising effect on radiation driven instabilities.

CHARGED PERFECT FLUID CONFIGURATIONS WITH A DILATON FIELD

We examine static charged perfect fluid configurations in the presence of a dilaton field. A method for construction of interior solutions is given. An explicit example of an interior solution which matches continuously the external Gibbons–Maeda–Garfinkle–Horowitz–Strominger solution is presented. Extremely charged perfect fluid configurations with a dilaton are also examined. We show that there are two types of extreme configurations. For each type the field equations are reduced to a single nonlinear equation on a space of a constant curvature. In the particular case of a perfect fluid with a linear equation of state, the field equations of the first type configurations are reduced to a Helmholtz equation on a space with a constant curvature. An explicit example of an extreme configuration is given and discussed.

A Generalized Method for Constructing Perfect-Fluid Solutions of Einstein's Equations

Using a 3-dimensional formulation of general relativity for non-empty spacetimes admitting a non-null Killing field, a transformation for generating new non-vacuum solutions of Einstein’s equations and its specialization to perfect-fluid configurations is presented. Assuming that the twist of the Killing field is a gradient, it is shown that the transformation can be applied to generate possibly new perfect-fluid solutions only when a strong restriction on the equation of state is imposed (i.e. ρ +3 P =0o rρ = P )or, alternatively, for the case of static spacetimes. Furthermore, the relation of the described technique to some previously known methods is given. In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions can be written in a singe compact form.

Cracking of Homogeneous Self-Gravitating Compact Objects Induced by Fluctuations of Local Anisotropy

We discuss the effect that small fluctuations of local anisotropy (principal stresses unequal) may have on the occurrence of cracking in spherical compact objects. Two families of homogeneous fluid distributions are considered. For both it is shown that departures from equilibrium may lead to the appearance of cracking, only if fluctuations of local anisotropy are allowed. The case of fluctuations in an initially locally isotropic (perfect fluid) configuration deserves particular attention.

Generating new perfect-fluid solutions from known ones

Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the stationary Killing field are functionally independent. It has been pointed out earlier by one of us (IR) that for these perfect-fluid geometries some of the basic field equations are invariant under an transformation. Here it is shown that this transformation can be applied to generate possibly new perfect-fluid solutions from existing known ones only for the case of a barotropic equation of state . In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions could be written in a singe compact form. A new derivation of all Petrov type D stationary axisymmetric rigidly-rotating perfect-fluid solutions with an equation of state is given in an appendix.

The asymptotical solutions near the singular points for perfect fluid configurations in the conformal Poincaré-gauge theory of gravitation

The asymptotical solutions describing the behaviour of a perfect fluid near the singular points in the conformal Poincaré-gauge theory of gravitation are obtained. The following type of equations of state occur at the center points of astrophysical objects: ultrarelativistic matter, quark matter, astrophysical vacuum.

On spherically symmetric shear-free perfect fluid configurations (neutral and charged). III. Global view

The topology of the solutions derived in Part I [J. Math. Phys. 28, 1118 (1987)] is discussed in detail using suitable topological embeddings. It is found that these solutions are homeomorphic to S3×R, R4, or S2×R2. Singularities and boundaries in these manifolds are examined within a global framework. One of these boundaries (mentioned but not examined in Part II) is regular (though unphysical), and is associated with an ‘‘asymptotically de Sitter’’ behavior characterized by an exponential form of the Hubble scale factor. Solutions with S2×R2 topology lack a center of symmetry [fixed point of SO(3)] and present a null boundary at an infinite affine parameter distance along hypersurfaces orthogonal to the four-velocity. This boundary, which in most cases is singular, can be identified as a null ℐ surface arising as an asymptotical null limit of timelike hypersurfaces. Solutions with this topology, matched to a Schwarzschild or Reissner–Nordstro/m region, describe collapsing fluid spheres whose ‘‘surface’’ (as seen by observers in the vacuum region) has finite proper radius, but whose ‘‘interior’’ is a fluid region of cosmological proportions. In the case when the null boundary of the fluid region is singular, it behaves as a sort of ‘‘white hole.’’ Uniform density solutions which are not conformally flat are all homeomorphic to S2×R2. Conformally flat solutions are also examined in detail. Their global structure has common features with those of FRW and de Sitter solutions. The static limits of all nonstatic solutions are discussed. In particular, under suitable parameter restrictions, some of these static solutions, together with the nonstatic conformally flat subclass, are the less physically objectionable of all solutions. Hence, it is suggested that kinetic theory models could be applied to them. Possible cosmological applications are discussed. The global structure of Wyman’s and McVittie’s solutions is examined in the Appendices.