A uniparametric perfect fluid solution to represent compact stars

In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio [Formula: see text]. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index [Formula: see text] guarantees the stability. In addition, the graph of [Formula: see text] versus [Formula: see text] shows a quasi-linear relationship for the equation of state [Formula: see text], which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of [Formula: see text] and a radius [Formula: see text], the model shows that the maximum central density occurs for a maximal compactness value [Formula: see text].

The cosmological constant as a zero action boundary

ABSTRACT The cosmological constant Λ is usually interpreted as Dark Energy (DE) or modified gravity (MG). Here, we propose instead that Λ corresponds to a boundary term in the action of classical General Relativity. The action is zero for a perfect fluid solution and this fixes Λ to the average density ρ and pressure p inside a primordial causal boundary: Λ = 4πG <ρ+3p >. This explains both why the observed value of Λ is related to the matter density today and also why other contributions to Λ, such as DE or MG, do not produce cosmic expansion. Cosmic acceleration results from the repulsive boundary force that occurs when the expansion reaches the causal horizon. This universe is similar to the ΛCDM universe, except on the largest observable scales, where we expect departures from homogeneity/isotropy, such as CMB anomalies and variations in cosmological parameters indicated by recent observations.

An anisotropic model for represent compact stars

Starting from a perfect fluid solution we constructed a generalization with anisotropic pressures and regular geometry as well as the pressures, the density and the speed of sound, these are also positive and monotonic decreasing functions. The speed of sound is lower than the speed of light, that is to say, the condition of causality is not broken. The model satisfies all the energy conditions and the radial [Formula: see text] and tangential [Formula: see text] speeds and complies with [Formula: see text] because of this the solution is stable according to the stability criteria related with the concept of cracking. The maximum value of the compactness factor [Formula: see text] which is lower than the Buchdahl limit and associated to neutron stars. In a complementary manner, we realize an analysis of the behavior of a star with a mass of [Formula: see text], with a fixed value of the anisotropy parameter and different compactness values, giving as a result that their central density [Formula: see text] and the superficial density [Formula: see text], the maximum values match the value of greater compactness of the model with a stellar radius of 6506.921 m.

A charged perfect fluid solution

A static and spherically symmetric stellar model is described by a perfect charged fluid. Its construction is done using the solution of the Einstein–Maxwell equations for which we specify the temporal metric and the electric field which is a monotonic increasing function null in the center. The density, pressure and speed of sound turn out to be regular functions, positive and monotonic decreasing as function of the radial distance. Also, the speed of sound is lower than the speed of light, that is to say, it does not violate the condition of causality. The value of compactness [Formula: see text], so the model is useful to represent neutron stars of quark stars. In a complementary manner, we report the physical values when describing a star of mass [Formula: see text] and radius [Formula: see text], in such case [Formula: see text], and given the presence of the charge, the interval for the central density [Formula: see text].

Relativistic anisotropic models for compact star with equation of state p = f(ρ)

We present new anisotropic models for Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] type perfect fluid solution. For this purpose, we started with metric potential [Formula: see text] same as Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] and [Formula: see text] is monotonically increasing function as suggested by Lake [K. Lake, Phys. Rev. D 67 (2003) 104015]. After that we determine the new pressure anisotropy factor [Formula: see text] with the help of both the metric potentials [Formula: see text] and [Formula: see text] and propose new well behaved general solution for anisotropic fluid distribution. The physical quantities like energy density, radial and tangential pressures, velocity of sound and redshift etc. are positive and finite inside the compact star. In this connection, we have studied the stability of the models, which is most vital one and also we determined the equation of state [Formula: see text] for the realistic compact star models. It is noted that the mass and radius of our models can represent the structure of realistic astrophysical objects such as Her X-1 and RXJ 1856-37.

Cosmological models through spatial Ricci-flow

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding.

On several static cylindrically symmetric solutions of the Einstein equations

We study the Einstein equations in the static cylindrically symmetric case with the stress–energy tensor of the form [Formula: see text], where [Formula: see text] is an unknown function and [Formula: see text], [Formula: see text], [Formula: see text] are arbitrary real constants ([Formula: see text] is assumed to be nonzero). The stress–energy tensor of this form includes as special cases several well-known solutions, such as the perfect fluid solution with the barotropic equation of state, the solution with the static electric field and the solution with the massless scalar field. We solve the Einstein equations with this stress–energy tensor and study some properties of the obtained metric.

MODELING USUAL AND UNUSUAL ANISOTROPIC SPHERES

In this paper, we study anisotropic spheres built from known static spherical solutions. In particular, we are interested in the physical consequences of a "small" departure from a physically sensible configuration. The obtained solutions smoothly depend on free parameters. By setting these parameters to zero, the starting seed solution is regained. We apply our procedure in detail by taking as seed solutions the Florides metrics, and the Tolman IV solution. We show that the chosen Tolman IV solution, and also the Heint IIa and Durg IV,V perfect fluid solutions, can be used to generate a class of parametric solutions where the anisotropic factor has features recalling boson stars. This is an indication that boson stars could emerge by "perturbing" appropriately a perfect fluid solution (at least for the seed metrics considered). Finally, starting with the Tolman IV, Heint IIa and Durg IV,V solutions, we build anisotropic gravastar-like sources with the appropriate boundary conditions.

PETROV TYPE I, STATIONARY, AXISYMMETRIC, PERFECT FLUID SOLUTION OF EINSTEIN'S EQUATIONS

We present a four-parameter, algebraically general solution for the interior of a rigidly rotating, axisymmetric perfect fluid, with the equation of state μ = p + const . The solution is analytically simple and has a static limit.