Anisotropic Fluid Model Research Articles

NEW SPHERICALLY SYMMETRIC ANISOTROPIC NEUTRON STAR MODEL USING FIELD EQUATIONS

In this paper, we obtain a new static spherically symmetric anisotropic fluid model of a neutron star in curvature coordinates. We consider , where , by taking the value of parameter in Durgapal solutions (Durgapal, 1982). The energy density, radial pressure, tangential pressure, and redshift are positive finite, and decreasing with respect to the increasing radius in this model. The pressure and density also decrease from the inner core to the crust of the object. We obtain this model by the specific choice of the constants and the anisotropy factor . The central value of the anisotropy factor is zero due to the perfect fluid nature at the center of the anisotropic model and it is increasing with the increasing radius. In our analysis we take and The model well behaves for the anisotropic neutron stars, which is shown analytically and graphically. The solution is free from any central singularity. We take realistic objects such as EXO 1785-248, SMC X-1, Her X-1, 4U 1538-52, LMC X-4, RX J1856-37, Cen X-3, PSR J1903-327, and Vela X-1 to represent our solutions graphically and numerically. We obtain this solution for for the first time. Therefore, the solution is quite new and derived for the first time.

Vaidya-Tikekar type anisotropic fluid model by gravitational decoupling

In this paper, a new interior solution for compact objects has been obtained using the minimal geometric deformation (MGD) approach along with the embedding Class I condition. Using MGD, the original system gets split into two parts, one of them is called the Einstein system and another one is the quasi-Einstein system for the extra source The Einstein system is solved by using the Vaidya-Tikekar metric along with the Class I condition, while for the quasi-Einstein system, the mimic approach for density constraint has been used such that A detailed physical analysis has been done as well as the physical viability of the model in terms of the thermodynamical variables, and different stability factors are also tested. Furthermore, the mass-radius ratio is also calculated for 12 different stars for different values of the decoupling constant which determines how the gravitational decoupling influences the compactness.

Vacuum self similar anisotropic cosmologies in F(R)-gravity

The implications from the existence of a proper Homothetic Vector Field (HVF) on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are studied. The fact that \emph{every} Spatially Homogeneous vacuum model is equivalent, formally, with a "flux" -free anisotropic fluid model in standard gravity and the induced power-law form of the functional $F(R)$ due to self-similarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions in proper $F(R)-$gravity (i.e. $R\neq 0$) strengthens the belief that curvature corrections will prevent the shear influence into the past thus permitting an isotropic singularity. We also discuss certain issues regarding the lack of vacuum models of type III, IV, VII$_{h}$ in comparison with the corresponding results in standard gravity.

Anisotropic fluid modeling of ionospheric upflow: Effects of low‐altitude anisotropy and thermospheric winds

AbstractA new anisotropic fluid model is developed to describe ionospheric upflow responses to magnetospheric forcing by electric fields and broadband ELF waves at altitudes of 90–2500 km. This model is based on a bi‐Maxwellian ion distribution and solves time‐dependent, nonlinear equations of conservation of mass, momentum, parallel energy, and perpendicular energy for six ion species important to E, F, and topside ionospheric regions. It includes chemical and collisional interactions with the neutral atmosphere, photoionization, and electron impact ionization. This model is used to examine differences between isotropic and anisotropic descriptions of ionospheric upflow driven by DC electric fields, possible effects of low‐altitude (<500 km) wave heating, and impacts of neutral winds on ion upflow. Results indicate that isotropic models may overestimate field‐aligned ion velocity responses by as much as ∼48%. Simulations also show significant ionospheric responses at low altitudes to wave heating for very large power spectral densities, but ion temperature anisotropies below the F region peak are dominated by frictional heating from DC electric fields. Neutral winds are shown to play an important role regulating ion upflow. Thermospheric winds can enhance or suppress upward fluxes driven by DC and BBELF fields by 10–20% for the cases examined. The time history of the neutral winds also affects the amount of ionization transported to higher altitudes by DC electric fields.

A New Charged Anisotropic Compact Star Model in General Relativity

In the present article, we explore a new static, spherically symmetric charged anisotropic fluid model of compact star in curvature coordinates. We consider metric potential g44 of Durgapal’s fifth solution [1] with a specific choice of electric field intensity E and physically acceptable expression of anisotropy factor Δ , which involve parameters K (charge) and Δ (anisotropy) respectively. The solution so obtained is utilized to construct the model for superdense star like neutron star. We have analysed that corresponding to X=0.1, K=2.8, a=1.6 and by assuming surface density , the mass of the compact star comes out to be with radius 14.51 kms, which closely resembles to that of PSRJ0348 + 0432. The solution is well behaved for the values of K satisfying 1≤K5. Our model is described analytically as well as with the help of graphical representations. Our solution is well behaved and free from any central singularity. It also satisfies all the energy conditions as well as the causality condition thus reconfirming the stability of our model.

Relativistic model of anisotropic charged fluid sphere in general relativity

In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity $E$ and pressure anisotropy factor $\Delta$ which involve parameters $K$ (charge) and $\alpha$ (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353–359, 2010). Our solution is well behaved in all respects for all values of $X$ lying in the range $0< X \leq 0.18$ , $\alpha$ lying in the range $0 \leq \alpha \leq6.6$ , $K$ lying in the range $0< K \leq 6.6$ and Schwarzschild compactness parameter “ $u$ ” lying in the range $0< u \leq 0.38$ . Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to $X=0.088$ , $\alpha=0.6$ and $K=4.3$ for which $u=0.2054$ and by assuming surface density $\rho_{b} = 4.6888 \times 10^{14}~\mbox{g/cm}^{3}$ the mass and radius are found to be $1.51~M_{\varTheta}$ and 10.90 km respectively. Assuming surface density $\rho_{b} = 2 \times 10^{14}~\mbox{g/cm}^{3}$ the mass and radius for a neutron star candidate are found to be $2.313~M_{\varTheta}$ and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.

A class of relativistic anisotropic charged stellar models in isotropic coordinates

In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters: 4<n≤21.6, 0<K<0.2499, 0≤α≤0.068 and Schwarzschild parameter, 0≤u=GM/c 2 R≤0.334. With Δ=0 we rediscover the isotropic model of Pant et al. (Astrophys. Space Sci. 352:135, 2014) and with α=0 and K=0 we rediscover the isotropic neutral model of Murad and Pant (Astrophys. Space Sci. 350:349, 2014). It has been observed that with the increase of α maximum mass decreases. We also present models of super dense star like neutron and quark star based on the particular solution taking n=4.35, α=0.002, K=0.2062 for which u has maximum value u max=0.306. By assuming surface density ρ b =4.6888×1014 g cm−3 the resulting well behaved solution has a maximum quark star mass M=2.02 M ⊙ and radius R=9.78 km; and the choice ρ b =2.7×1014 g cm−3 results charged fluid ball of maximum mass M=2.66 M ⊙ and radius R=12.89 km.

A weakly nonlocal anisotropic fluid model for inhomogeneous Stokesian suspensions

A continuum model is proposed for a weakly inhomogeneous Stokesian suspensions, as an extension with minor amendments of a previous work on homogeneous suspensions [J. D. Goddard, J. Fluid Mech. 568, 1 (2006)]. In the present model, stress and particle flux are given as invariant tensor functions of particle volume fraction ϕ, deformation rate E, and second-rank anisotropy tensor A, in a form that is also linear in E and the gradients of ϕ, E, and A. In contrast to models without history dependence, all nonlinear dependence of particle flux on E arises from the evolution of A. Detailed attention is paid to unsteady viscometric flow, where a contribution of streamline curvature to particle migration emerges as a natural consequence of tensorial gradients. The model predicts equal curvature-induced fluxes in gradient and vorticity directions but there is an unexplained disagreement with recent experiments on Couette and torsional flows. A previously proposed corotational evolution equation for A, with a two-mode exponential relaxation, is employed to investigate the transient response following the reversal of shearing in sinusoidal and in steady shear. The model predicts roughly equal response for the two flows if sinusoidal strains are of order unity, which is consistent with some but not all experiments. The model for particle flux admits an asymmetric diffusion tensor which, owing to Stokesian reversibility, can become nonpositive upon abrupt reversal of shearing. This effect is diminished by non-Stokesian response on short strain scales, which, although poorly understood, appears essential to elementary models without dependence on shear history. A synthesis is given of multipolar Stokesian resistance and the associated Stokesian dynamics, showing how these follow from a single grand resistance kernel. In addition to unifying and extending large literature on Stokesian resistance formulae, this provides some justification for the proposed continuum model and possible multipolar extensions.

Neutral perfect fluids and charged thin shells with electromagnetic mass in general relativity

We build extended sources for the Reissner-Nordström metric. Our models describe a neutral perfect fluid core bounded by a charged thin shell, and feature everywhere positive rest mass density and everywhere non-negative active gravitational mass, as well as classical electron radius and electromagnetic total mass. We contrast our results with previously discussed charged anisotropic fluid models which excluded the thin shell and presented similar properties. Our charged thin shells are restricted by the 2D texture equation of state which causes the continuity of the active gravitational mass, in spite of the singularity of the energy-momentum tensor. We mention possible extensions of this study suggested by modified active mass formulae proposed in the literature.

General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

Einstein’s spherically symmetric interior gravitational equations are investigated. Following Synge’s procedure, the most general solution of the equations is furnished in case T11 and T44 are prescribed. The existence of a total mass function, M(r,t), is rigorously proved. Under suitable restrictions on the total mass function, the Schwarzschild mass M(r,t)=m, implicitly defines the boundary of the spherical body as r=B(t). Both Synge’s junction conditions as well as the continuity of the second fundamental form are examined and solved in a general manner. The weak energy conditions for an arbitrary boost are also considered. The most general solution of the spherically symmetric anisotropic fluid model satisfying both junction conditions is furnished. In the final section, various exotic solutions are explored using the developed scheme including gravitational instantons, interior T-domains, and D-dimensional generalizations.

Shear-free, irrotational, geodesic, anisotropic fluid cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form , with , then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

On spacetimes admitting shear-free, irrotational, geodesic time-like congruences

A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic time-like congruence is presented. The equations governing the models for a general energy--momentum tensor are written down. Coordinates in which the metric of such spacetimes takes on a simplified form are established. The general subcases of `zero anisotropic stress', `zero heat-flux vector' and `two-component fluids' are investigated. In particular, perfect-fluid Friedmann--Robertson--Walker models and spatially homogeneous models are discussed. Models with a variety of physically relevant energy--momentum tensors are considered. Anisotropic fluid models and viscous fluid models with heat conduction are examined. Also, models with a perfect fluid plus a magnetic field or with pure radiation, and models with two non-collinear perfect fluids (satisfying a variety of physical conditions) are investigated. In particular, models with a (single) perfect fluid which is tilting with respect to the shear-free, vorticity-free and acceleration-free time-like congruence are discussed.

Flow properties of superfluid systems of fermions

The nonspherically symmetric solutions to the Bardeen-Cooper-Schrieffer theory are given a physical interpretation in terms of an anisotropic fluid model. These solutions have been used previously to predict a phase transition in liquid by He{sup 3} by Emery and Sessler and Anderson, Morel, Brueckner, and Soda. An investigation of the flow properties of such systems is made that involves the calculation of the effective mass for flow in a straight channel and the moment of inertia of a cylindrical container of the liquid. The angular dependent energy-gap characteristic of this type of theory leads to an effective mass for flow that depends on the angle between the axis of symmetry of the fluid and the direction of flow. It also vanishes as the absolute temperature tends to zero, although not as rapidly as for a spherically symmetric gap. The moment of inertia, when the symmetry direction for the fluid and the rotation axis are the same, is simply related to the mass for flow.