Stability analysis of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-AdS black holes

We study the stability of the f(R)-AdS (Schwarzschild–AdS) black hole obtained from f(R) gravity. In order to resolve the difficulty of solving fourth-order linearized equations, we transform f(R) gravity into scalar–tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a dynamical scalaron, showing that all linearized equations are second order. Using the positivity of gravitational potentials and S-deformed technique allows us to guarantee the stability of f(R)-AdS black hole if the scalaron mass squared satisfies the Breitenlohner–Freedman bound. This is confirmed by computing quasinormal frequencies of the scalaron for the f(R)-AdS black hole.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) global monopole revisited

In this paper the f(R) global monopole is reexamined. We provide an exact solution for the modified field equations in the presence of a global monopole for regions outside its core, generalizing previous results. Additionally, we discuss some particular cases obtained from this solution. We consider a setup consisting of a possible Schwarzschild black hole that absorbs the topological defect, giving rise to a static black hole endowed with a monopole’s charge. Besides, we demonstrate how the asymptotic behavior of the Higgs field far from the monopole’s core is shaped by a class of spacetime metrics which includes the ones analyzed here. In order to assess the gravitational properties of this system, we analyze the geodesic motion of both massive and massless test particles moving in the vicinity of such configuration. For the material particles we set the requirements they have to obey in order to experience stable orbits. On the other hand, for the photons we investigate how their trajectories are affected by the gravitational field of this black hole.     

Energy distribution in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

The well-known energy problem is discussed in f (R) theory of gravity. We use the generalized Landau–Lifshitz energy–momentum complex in the framework of metric f (R) gravity to evaluate the energy density of plane symmetric solutions for some general f (R) models. In particular, this quantity is found for some popular choices of f (R) models. The constant scalar curvature condition and the stability condition for these models are also discussed. Further, we investigate the energy distribution of cosmic string spacetime.     

Complexity growth rates for AdS black holes in massive gravity and <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The “complexity = action” duality states that the quantum complexity is equal to the action of the stationary AdS black hole within the Wheeler–DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr–Newman black holes in f(R) gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.     

Horizon thermodynamics in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) theory

We investigate whether the new horizon first law proposed recently still work in f(R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in f(R) theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in f(R) theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.     

Geodesic deviation equation in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In this paper we study the Geodesic Deviation Equation (GDE) in metric f (R) gravity. We start giving a brief introduction of the GDE in General Relativity in the case of the standard cosmology. Next we generalize the GDE for metric f (R) gravity using again the FLRW metric. A generalization of the Mattig relation is also obtained. Finally we give and equivalent expression to the Dyer-Roeder equation in General Relativity in the context of f (R) gravity.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Cosmology from <Emphasis Type="Italic">q</Emphasis>-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by q ^(a) with label a), we have obtained, in the low-energy limit, a particular type of f(R) model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological f(R) models on physical grounds. The text was submitted by the authors in English.     

The Post-Minkowskian Limit of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-gravity

We formally discuss the post-Minkowskian limit of f(R)-gravity without adopting conformal transformations but developing all the calculations in the original Jordan frame. It is shown that such an approach gives rise, in general, together with the standard massless graviton, to massive scalar modes whose masses are directly related to the analytic parameters of the theory. In this sense, the presence of massless gravitons only is a peculiar feature of General Relativity. This fact is never stressed enough and could have dramatic consequences in detection of gravitational waves. Finally the role of curvature stress-energy tensor of f(R)-gravity is discussed showing that it generalizes the so called Landau-Lifshitz tensor of General Relativity. The further degrees of freedom, giving rise to the massive modes, are directly related to the structure of such a tensor.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity solutions for evolving wormholes

The scalar–tensor f(R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f(R) gravity formalism. These f(R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit \(f(R)=R,\) NEC can be violated at large in regions around the throat.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Exploring plane-symmetric solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

Non-vacuum Bianchi types <Emphasis Type="Italic">I</Emphasis> and <Emphasis Type="Italic">V</Emphasis> in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In a recent paper (Sharif and Shamir in Class. Quantum Grav. 26:235020, 2009), we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f (R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

Conformally flat collapsing stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The present work includes an analytical investigation of a collapsing spherical star in f(R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration and the loss of energy through a heat conduction forces the rate of the collapse to die down and the formation of a zero proper volume singularity is realized only asymptotically.     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.     

Solutions for <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity coupled with electromagnetic field

In the presence of external, linear/nonlinear electromagnetic fields we integrate \(f(R)\sim R+2\alpha \sqrt{R+\mathrm{const.}}\) gravity equations. In contrast to their Einsteinian cousins the obtained black holes are non-asymptotically flat with a deficit angle. In proper limits we obtain from our general solution the global monopole solution in f(R) gravity. The scale symmetry breaking term adopted as the nonlinear electromagnetic source adjusts the sign of the mass of the resulting black hole to be physical.     

Bianchi V cosmological model in Palatini <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We apply the dynamical systems approach to investigate the spatially homogeneous and anisotropic Bianchi type V models for the Palatini version of f(R) gravity. In particular, we examine the existence of equilibrium points along with their exact solutions and stability properties for two different forms of f(R). Moreover, the evolution of shear and spatial curvature by performing the phase space analysis are studied and also the phases of evolution from anisotropic universe to the stable de-Sitter flat universe are discussed.