Related papers: On "hard stars" in general relativity
We study spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations. Equilibria are given as solutions of the Lane-Emden equations, and the linearized equation around one of these equilibria admits time-periodic…
We present a class of new relativistic solutions with anisotropic fluid for compact stars in hydrostatic equilibrium. The interior space-time geometry considered here for compact objects are described by parameters namely, $\lambda$, $k$,…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
Binary neutron star mergers produce massive, hot, rapidly differentially rotating neutron star remnants; electromagnetic and gravitational wave signals associated with the subsequent evolution depend on the stability of these remnants.…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…
In this article we study the structure and stability of compact astrophysical objects which are ruled by the dark energy equation of state (EoS). The existence of dark energy is important for explaining the current accelerated expansion of…
In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al.[1] algorithm. The anisotropic fluid solution so obtained join continuously to…
We consider stability of rotating gaseous stars modeled by the Euler-Poisson system with general equation of states. When the angular velocity of the star is Rayleigh stable, we proved a sharp stability criterion for axi-symmetric…
By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$…
The accurate determination of the maximum mass of the neutron stars is one of the most important tasks in astrophysics. It is directly related to the identification of the black holes in the universe, the production of neutron stars from…
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitely computed and are simply written in terms of the oblate spheroidal…