Related papers: Study of polytropes with Generalized polytropic Eq…
The present status of the shear-free fluid conjecture in general relativity is discussed: a review is given of recent partial proofs, a new and complete proof is given for the case of a linear equation of state, including a non-zero…
We discuss the effect that small fluctuations of both local anisotropy and energy density, may have on the occurrence of cracking in spherical compact objects satisfying a polytropic equation of state. A systematic scheme to bring the fluid…
The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502…
We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a nonlocal equation of state. This equation relates, at a given point, the components of the corresponding…
We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…
The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…
In this paper we are concerned with the effects of anisotropic pressure on the boundary conditions of anisotropic Lane-Emden equation and homology theorem. Some new exact solutions of this equation are derived. Then some of the theorems…
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations…
The Ericksen-Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally well-posed…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
We investigate the impact of an external pressure on the structure of self-gravitating polytropes for axially symmetric ellipsoids and rings. The confinement of the fluid by photons is accounted for through a boundary condition on the…
We discuss the connection between logotropes and polytropes in astrophysics and cosmology. The logotropic equation of state $P=A\ln(\rho/\rho_P)$ may be seen as a degenerate form of the polytropic equation of state $P=K\rho^{\gamma}$ in the…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of…
Equations of state for a cold neutron star's interior are presented in three-column tables that relate the baryonic density, the energy density, and the pressure. A few analytical expressions for those tables have been established these…
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…
We study the conditions for stability of electrically charged, non-conductive perfect fluid tori with respect to linear perturbations. To this end we employ Lagrangian perturbation formalism and we assume a system where the fluid orbits a…
We consider the Einstein-Maxwell system of equations in the context of isotropic coordinates for matter distributions with anisotropy in the presence of an electric field. We assume a polytropic equation of state for the matter…
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…