Narrow Results

The purpose of this paper is to study the effects of dark energy on dynamics of the collapsing fluid within the framework of metric f(R) gravity. The fluid distribution is assumed to be locally anisotropic and undergoing dissipation in the form of heat flow, null radiations and shear viscosity. For this purpose, we take general spherical symmetric spacetime. Dynamical equations are obtained and also some special solutions are found by considering shearing expansion-free evolution of the fluid. It is found that dark energy affects the mass of the collapsing matter and rate of collapse but does not affect the hydrostatic equilibrium.

The aim of this paper is to find proper conformal vector fields of some Bianchi type II spacetimes in the f(R) theory of gravity using direct integration technique. In this study, seven cases have been discussed. Studying each case in detail, it is shown that the spacetimes under consideration do not admit proper conformal vector fields. Conformal vector fields are either homothetic vector fields or Killing vector fields.

In this study, we have investigated generalized anisotropic universe models for magnetized strange quark matter (MSQM) distribution in the framework of $f(R)$ gravitation theory. For this aim, we have used linearly varying deceleration parameter suggested by Akarsu and Dereli (2012) and equation of state for strange quark matter. For LRS Bianchi I universe model, the magnetic field was obtained as zero. But it was found to be different from zero for other universe models. Also, the geometric and physical aspects of the model are discussed in the conclusion.

We consider the modified f(R) theory of gravity whose higher-order curvature terms are interpreted as a gravitational fluid or dark source. The gravitational collapse of a spherically symmetric star, made up of locally anisotropic viscous fluid, is studied under the general influence of the curvature fluid. Dynamical equations and junction conditions are modified in the context of f(R) dark energy and by taking into account the expansionfree evolution of the self-gravitating fluid. As a particular example, the Skripkin model is investigated which corresponds to isotropic pressure with constant energy density. The results are compared with corresponding results in General Relativity.

In this paper, we examine the validity of the generalized second law (GSL) of gravitational thermodynamics in the context of interacting f(R) gravity. We take into account that the boundary of the universe to be confined by the dynamical apparent horizon in a flat FRW universe. We study the effective equation of state, deceleration parameter and GSL in this interaction-framework. We find that the evolution of the total entropy increases through the interaction term. As an example, we consider a f(R) gravity with a power-law dependence on the curvature R. Here, we find exact solutions for a model in which the interaction term is related to the total energy density of matter.

In this paper, we investigate the dynamics of charged cylindrical stellar collapsing model filled with bulk viscous dissipative fluid in $f(R)$ gravity. For this purpose, we formulate dynamical equations through Misner–Sharp technique and derive transport equation. Finally, we analyze the collapse rate by coupling the transport and dynamical equations. It is concluded that the collapse rate of charged cylindrical model slows down under the influence of dark source terms and matter variables.

This paper studies the collapse of stellar filaments in the presence of dark matter (DM). We use $f(R)$ gravity to involve DM in the collapse. We apply Darmois junction conditions (DJCs) on the surface of collapsing boundary $\mathrm{\Sigma }$ and obtain the collapse equation. The radial pressure associated with the seen matter is found to be nonzero at $\mathrm{\Sigma }$. We then use Starobinsky model, $f(R)=R+\alpha R^2$, as a candidate of DM to obtain stability criteria (SC) of the collapsing body. It is found that the stability of filamentary structure relates radial pressure of baryonic directly with the gravitational effects of DM. Stability of polytropic family of filaments are studied by applying polytropic equation of state to baryonic contribution. For all polytropic stable filaments, it turns out that the visible matter density is exponentially linked to effects of DM. Finally, we discuss connection between exotic terms and gravitational waves (GW). It is theoretically indicated that the presence of DM can affect the GW propagation.

A classification of static spherically symmetric space-times in $f(R)$ theory of gravity according to their conformal vector fields (CVFs) is presented. For this analysis, a direct integration technique is used. This study reveals that for static spherically symmetric space-times in $f(R)$ theory of gravity, CVFs are just Killing vector fields (KVFs) or homothetic vector fields (HVFs). For this classification, six cases have been discussed out of which there exists only one case for which CVFs become HVFs while in the rest of the cases CVFs become KVFs.

Nonstatic plane symmetric spacetimes are considered to study conformal vector fields (VFs) in the $f(R)$ theory of gravity. Firstly, we investigate some proper nonstatic plane symmetric spacetimes by solving the Einstein field equations (EFEs) in the $f(R)$ theory of gravity using algebraic techniques. Secondly, we find CVFs of the obtained spacetimes by means of the direct integration approach. There exist seven cases. Studying each case in detail, we find that the CVFs are of dimension three, five, six and fifteen.

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the $f(R)$ gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the $f(R)$ gravity.

In this paper, we examine massless scalar field by using unimodular $f(R)$ theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular $f(R)$ theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular $f(R)$ theory. Also, stiff fluid interpretation of scalar field is reviewed.