Narrow Results

Correlations in quantum fluids such as liquid ³He continue to be of high interest to scientists. Based on this prospect, the present work is devoted to study the effects of spin–spin correlation function on the thermodynamic properties of polarized liquid ³He such as pressure, velocity of sound, adiabatic index and adiabatic compressibility along different isentropic paths, using the Lennard–Jones potential and employing the variational approach based on cluster expansion of the energy functional. The inclusion of this correlation improves our previous calculations and leads to good agreements with experimental results.

We study the influence of interaction strengths on nuclear properties and global static properties of neutron stars with emphasis on the adiabatic index, considering also the constraint of chemical equilibrium and charge neutrality. We develop an equation of state (EoS) in the framework of an extended effective QHD model using a parameterized phenomenological Lagrangian density containing the fundamental baryon octet, the σ, ω and ϱ meson fields and the lightest charged leptons. The results of our approach show that, for a small range of values of the baryon–meson coupling parameters, we can consistently describe nuclear matter and the structure of neutron stars. Our results indicate that in the energy density range above hyperon thresholds, the behavior of the adiabatic index is roughly comparable to the corresponding one in the case of an extreme relativistic hydrodynamical perfect fluid.

The adiabatic index of pulsars formed by hadronic or quarkionic matter, with and without trapped neutrinos, is calculated for two values of the entropy per baryon S = 0, 2 k_B/baryon. The nonlinear Walecka model¹ is used to describe hadronic stars, and the MIT bag model² to describe quark stars. Particle fractions for each case are obtained and the appearance of particles are shown to coincide with drops in the adiabatic index.

In this work, we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection entries containing three independent metric functions is taken into account for establishment of instability range. Implementation of linear perturbation on constitutive modified dynamical equations yield evolution equation. This equation associates adiabatic index $\mathrm{\Gamma }$ with material and dark source components of physical parameters defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations. It is remarked that the axial system evolving under shear-free condition implicates high levels of stability in anisotropic environment.

In this paper, we have analyzed the dynamical stability of shearing viscous anisotropic fluid with cylindrical symmetry in $f(R,T)$ theory. We have chosen two viable $f(R,T)$ models for dynamical analysis, and explored their nature and role for stable stellar configuration. Modified field equations and corresponding dynamical equations have been constructed, perturbation approach is adopted to deal with complexity of these equations. With the help of perturbed dynamical equations, the evolution equation has been established to analyze the role of shear viscosity and pressure anisotropy on dynamics of cylindrical system. The adiabatic index $\mathrm{\Gamma }$ is used to investigate the instabilities appearing in Newtonian (N) and post-Newtonian (pN) approximations. Some conditions are found for material variables that are required to meet the stability criterion. We compare the outcomes of our analysis with the results of various models available in literature to reach at more comprehensive conclusion.

We present a family of relativistic fluid spheres using the Karmarkar criterion along with the Pandey–Sharma condition. Ranges of $n$ and $m$ for well-behaved solutions depend on the mass and radius of the compact star model. As an example, we have chosen Vela X-1 ($M=1.77{\mathrm{\text{M}}}_{\odot },R=9.56\mathrm{\text{km}}$) for complete analysis of the solutions. For the same star, the well-behaved ranges are $1<n<5$ and $3<m<13$. However, beyond these limits, either the transversal sound speed becomes imaginary or violates the causality principle. Further, the critical part of our solution is that corresponding to every nonzero positive even value of $m$ yields zero values of all the physical quantities.

This paper deals with stability analysis of anisotropic-charged cylindrical geometry coupled with $f(R,T)$ modified gravity theory (${ℳ}{𝒢}{𝒯}$). In this ${ℳ}{𝒢}{𝒯}$, the Lagrangian is a varying function of traces of Ricci and stress tensors. In order to examine the stable behavior of the anisotropic cylindrical cosmic object under the electromagnetic effects, we calculated the modified equations of motion and equations of continuity. in the background of $f(R,T)$ theory. By utilizing the perturbation technique, we constitute a modified collapse equation (${ℳ}{𝒞}{ℰ}$), which contains geometrical and physical variables in the charged scenario. Our investigation continues under the nonminimally coupled function of ${ℳ}{𝒢}{𝒯}$. Furthermore, we investigate the dynamically stable phases of charged geometry at Newtonian $({𝒩})$ and post-Newtonian ($p{𝒩}$) epochs with the help of the rigidity parameter of fluid ($\mathrm{\Gamma }$) by imposing some constraints on physical parameters.

This work is related to the stability of a nonstatic, very restricted class of axially symmetric cosmic matter configuration under the influence of modified gravitational theory (AGT) with a realistic model in anisotropic conditions. We construct dynamically modified equations, continuity equations, mass functions and collapse equations in the scenario of considered AGT. We continue our analysis under the influence of f(R,T) gravity along with a minimally coupled gravitational function of the form $f(R,T)=R+\beta R_c(1-{(1+\frac{R^2}{R_c^2})}^{-n})+\lambda T$, where $R_c$ indicates constant entity. In this gravitational model, f is a function of Ricci scalar invariant R and the trace of the stress–energy tensor T. This gravitational function gives significant findings only for $\beta >0,n>0$, and both belong to the set of positive real numbers and also $\lambda \ll 1$. We establish expressions of an adiabatic index, i.e. stiffness parameter of fluid $(\mathrm{\Gamma })$ utilizing relevant perturbation technique with the help of collapse equation in Newtonian $(\mathbb{N})$ and post-Newtonian $(\mathbb{P}\mathbb{N})$ domains. We consider the particular form of metric as well as material functions in $(\mathbb{N})$ and $(\mathbb{P}\mathbb{N})$ eras, and impose some constraints on physical quantities (i.e. pressure, density, mass, etc.) to carry out the stable behavior of a considered restricted geometry.

This paper aims to investigate the stability constraints under the influence of particular modified gravity theory $𝕄𝔾𝕋$, i.e. $f(R,T)$ gravity in which the Lagrangian is a varying function of $R$ and trace of energy momentum tensor ($T$). We examine stable behavior for compact cylindrical star having anisotropic symmetric configuration. We establish dynamical equations as well as equations of continuity in the background of this particular non-minimal coupled $𝕄𝔾𝕋$. We utilize perturbation technique which will be applied on geometrical as well as material physical quantities to constitute collapse equation. We continue this significant investigation to understand the dynamical behavior of considered cylindrical system under non-minimal coupled $f(R,T)$ functional, i.e. $f(R,T)=R+\xi R_c[1-{\{1+\frac{R^2}{R_c^2}\}}^{-n}]+\lambda RT$. This gravitational function gives compatible findings only for $\xi >0,n\in R^{+}$, also $0<\lambda \ll 1$ and $\lambda RT$ considered in this astrophysical model as coupling entity. This model contains $R_c$ which is constant entity, having the values of order of the effective Ricci scalar $R$. Furthermore, we impose some physical constraints to determine and maintain the stability criteria by establishing the expression of adiabatic index, i.e. $\mathrm{\Gamma }$ for cylindrical anisotropic configuration, in Newtonian $(N)$ and post-Newtonian ($pN$) eras.