Newman-Janis Ansatz for rotating wormholes

A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to generate solutions to the Einstein field equation inspired by the mention problems. We present a collection of independent classes of exact interior solutions of the Einstein equation describing rotating fluids with anisotropic pressures. Furthermore, we will elaborate on some obtained solutions by alluding to rotating wormholes.

Chaplygin strange stars in presence of quintessence

Starting from a regular, static and spherically symmetric spacetime, we present a stellar model formed by two sources of ordinary and quintessence matter both with anisotropic pressures. The ordinary matter, with density [Formula: see text], is formed by a fluid with a state equation type Chaplygin [Formula: see text] for the radial pressure. And the quintessence matter, with density [Formula: see text], has a state equation [Formula: see text] for the radial pressure and [Formula: see text] for the tangential pressure with [Formula: see text]. The model satisfies the required conditions to be physically acceptable and additionally the solution is potentially stable, i.e. [Formula: see text] according to the cracking concept, and it also satisfies the Harrison–Zeldovich–Novikov criteria. We describe in a graphic manner the behavior of the solution for the case in which the mass is [Formula: see text] and radius [Formula: see text][Formula: see text]km which matches the star EXO 1785-248, from where we obtain the maximum density [Formula: see text] for the values of the parameters [Formula: see text], [Formula: see text].

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.

Quintessences compact star with Durgapal potential

A compact star model formed by quintessence and ordinary matter is presented, both sources have anisotropic pressures and are described by linear state equations, also the state equation of the tangential pressure for the ordinary matter incorporates the effect of the quintessence. It is shown that depending on the compactness of the star [Formula: see text] the constant of proportionality [Formula: see text] between the density of the ordinary matter and the radial pressure, [Formula: see text], has an interval of values which is consistent with the possibility that the matter is formed by a mixture of particles like quarks, neutrons and electrons and not only by one type of them. The geometry is described by the Durgapal metric for [Formula: see text] and each one of the pressures and densities is positive, finite and monotonic decreasing, as well as satisfying the condition of causality and of stability [Formula: see text], which makes our model physically acceptable. The maximum compactness that we have is [Formula: see text], so we can apply our solution considering the observational data of mass and radii [Formula: see text], [Formula: see text] km which generate a compactness [Formula: see text] associated to the star PSR J0348[Formula: see text]+[Formula: see text]0432. In this case, the interval of [Formula: see text] and its maximum central density [Formula: see text] and in the surface [Formula: see text] of the star are [Formula: see text] and [Formula: see text], respectively, meanwhile the central density of the quintessence [Formula: see text].

Instability analysis of expansion-free sphere in f(𝒢) gravity

The aim of this paper is to study the dynamical instability of expansion-free spherically symmetric anisotropic fluid in the framework of [Formula: see text] gravity. We apply perturbation scheme of the first-order to the metric functions as well as matter variables and construct modified field equations for both static and perturbed configurations using power-law [Formula: see text] model. To discuss the instability dynamics, we use the contracted Bianchi identities to formulate the dynamical equations in both Newtonian and post-Newtonian regimes. It is found that the range of instability is independent of adiabatic index for expansion-free fluid but depends on anisotropic pressures, energy density and Gauss–Bonnet (GB) terms.

On Slowly Rotating Magnetized White Dwarfs

Rotating magnetized white dwarfs are studied within the framework of general relativity using Hartle’s formalism. Matter inside magnetized white dwarfs is described by an equation of state of particles under the action of a constant magnetic field which introduces anisotropic pressures. Our study is done for values of magnetic field below [Formula: see text] G - a threshold of the maximum magnetic field obtained by the cylindrical metric solution - and typical densities of WDs. The effects of the rotation and magnetic field combined are discussed, we compute relevant magnitudes such as the moment of inertia, quadrupole moment and eccentricity.

On the stability of (M theory) stars against collapse: Role of anisotropic pressures

Unitarity of evolution in gravitational collapses implies existence of macroscopic stable horizonless objects. With such objects in mind, we study the effects of anisotropy of pressures on the stability of stars. We consider stars in four or higher dimensions and also stars in M theory made up of (intersecting) branes. Taking the stars to be static, spherically symmetric and the equations of state to be linear, we study “singular solutions” and the asymptotic perturbations around them. Oscillatory perturbations are likely to imply instability. We find that nonoscillatory perturbations, which may imply stability, are possible if an appropriate amount of anisotropy is present. This result suggests that it may be possible to have stable horizonless objects in four or any higher dimensions, and that anisotropic pressures may play a crucial role in ensuring their stability.

PRESENCE OF ANISOTROPIC PRESSURES IN LEMAÎTRE–TOLMAN–BONDI COSMOLOGICAL MODELS

We describe Lemaître–Tolman–Bondi cosmological models where an anisotropic pressure is considered. By using recent astronomical observations coming from supernova of Ia types, we constraint the values of the parameters that characterize our models.