Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Noether gauge symmetry for f(R) gravity in Palatini formalism

In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini f(R) theory of gravity. Using the dynamical equivalence between f(R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f(R) Lagrangian we find out the form of f(R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f(R) yield a power-law expansion for the scale factor of the universe.     

Higher-dimensional perfect fluid collapse in $$ gravity

In this paper, we analyze higher-dimensional spherical perfect fluid collapse in \(f(R,T)\) theory for minimally coupled models. We use Darmois junction conditions by taking Lemaître-Tolman-Bondi geometry as an interior region and Schwarzschild metric as an exterior spacetime. The solution of field equations is obtained for constant scalar curvature. We determine mass in two regions of the collapsing object and discuss the formation of apparent horizons. We conclude that modified curvature term tends to slow down the collapse rate.     

Non-vacuum solutions of Bianchi type VI0 universe in f(R) gravity

In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI ₀ spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the source of matter and dark energy. The physical behavior of these solutions is analyzed and compared in the future evolution with the help of some physical and geometrical parameters. It is concluded that in the presence of isotropic fluid, the model has singularity at [(t)\tilde]=0\tilde{t}=0 and represents continuously expanding shearing universe currently entering into phantom phase. In anisotropic fluid, the model has no initial singularity and exhibits the uniform accelerating expansion. However, the spacetime does not achieve isotropy as t→∞ in both of these solutions.     

Gravitational charged perfect fluid collapse in Friedmann universe models

This paper is devoted to the study of gravitational charged perfect fluid collapse in Friedmann universe models with cosmological constant. For this purpose, we assume that the electromagnetic field is so weak that it does not introduce any distortion into the geometry of the spacetime. The results obtained from the junction conditions between the Friedmann and the Reissner–Nordström de Sitter spacetimes are used to solve the field equations. Further, the singularity structure and mass effects of the collapsing system on the time difference between the formation of apparent horizons and singularity have been studied. This analysis provides the validity of the Cosmic Censorship Hypothesis. It is found that the electromagnetic field affects the area of apparent horizons and their time of formation.     

Quadrupolar gravitational radiation as a test-bed for f(R)-gravity

The debate concerning the viability of f(R)-gravity as a natural extension of General Relativity could be realistically addressed by using results coming from binary pulsars like PSR 1913 + 16. To this end, we develop a quadrupolar approach to the gravitational radiation for a class of analytic f(R)-models. We show that experimental results are compatible with a consistent range of f(R)-models. This means that f(R)-gravity is not ruled out by the observations and gravitational radiation (in strong field regime) could be a test-bed for such theories.     

Gravitational collapse in generalized Vaidya space-time for Lovelock gravity theory

In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in (n+2)-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.     

Cosmic acceleration and phantom crossing in f(T)-gravity

In this paper, we propose two new models in f(T) gravity to realize universe acceleration and phantom crossing due to dark torsion in the formalism. The model parameters are constrained and the observational test are discussed. The best fit results favors an accelerating universe with possible phantom crossing in the near past or future followed respectively by matter and radiation dominated era.     

Gravitational collapse of a self-gravitating unidirectional fluid flow

This paper explores the collapsing process of a unidirectional isotropic matter configuration. The junction conditions for a static exterior geometry and the non-static interior geometry are expressed in terms of the cosmological constant. The time-lapse for the appearance of the black hole and the cosmological horizon is calculated. It is observed that in the de-Sitter space, the unidirectional perfect fluid flow does not make the collapse disappear. The vacuum energy of the cosmological constant makes the collapsing process quite slow and affects the time-lapse of horizon formation. Moreover, the presence of string tension increases the time-lapse of horizon formation.     

Gravitational radiation from an isolated perfect fluid in higher multipole moments

The purpose of this paper is to give the unknown angular momentum loss of an isolated perfect fluid in any higher multipole moments in the linear approximation of general relativity theory. Also, we discuss the energy and linear momentum fluxes of the given source in higher multipole moments.     

Bianchi type-VI0 perfect fluid cosmological model in a modified theory of gravity

A spatially homogeneous and anisotropic Bianchi type-VI₀ space-time filled with perfect fluid in general relativity and also in the framework of f(R,T) gravity proposed by Harko et al. (in arXiv:1104.2669 [gr-qc], 2011) has been studied with an appropriate choice of the function f(R,T). The field equations have been solved by using the anisotropy feature of the universe in Bianchi type-VI₀ space time. Some important features of the models, thus obtained, have been discussed. We noticed that the involvement of new function f(R,T) doesn’t affect the geometry of the space-time but slightly changes the matter distribution.     

Inhomogeneous perfect fluid cosmologies in (4+1) dimensions

Exact solutions are obtained in (4+1) dimensions for plane symmetric and cylindrically symmetric inhomogeneous spacetimes. In the former case the three space depends on time only while the metric corresponding to the extra dimension is dependent on space as well as time coordinates. The cylindrically symmetric nonstatic solutions for the perfect fluid have no singularity near the axis, but show big bang type of singularity in the finite past. One of the classes of such solutions satisfies the barotropic equation of state of the form =p. Static solutions with cylindrically symmetric solutions are also obtained in 5 dimensions.     

A comparison of the spectral characteristics of the Wolf Sunspot Number (RZ) and Group Sunspot Number (RG)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

Newtonian and post Newtonian expansionfree fluid evolution in f(R) gravity

We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of f(R) gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the collapsing fluid, Newtonian and post Newtonian regimes are taken into account. The field equations are investigated for a well-known f(R) model of the form R+δR ² admitting Schwarzschild solution. The perturbation scheme is used on the dynamical equations to explore the instability conditions of expansionfree fluid evolution. We conclude that instability conditions depend upon pressure anisotropy, energy density and some constraints arising from this theory.     

Gravitational collapse in free fall of a slowly rotating star

The gravitational collapse of a slowly rotating star with small deviations from spherical symmetry is studied. The exterior metric is chosen to be the Kerr metric in synchronous coordinates discarding terms of order (a/r)². Interior geometry is constructed by adding an off-diagonal term in first order ofa to the exact solution of the non-rotating case. This term is determined in part by requiring the validity of the junction conditions at the star's surface and by demanding that the angular momentum of the source is equal toM A, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid which rotates nonuniformly relative to the synchronous frame which is no longer comoving the stellar matter.     

Bianchi type VI h perfect fluid cosmological model in f(R,T) theory

In this paper, we have investigated Bianchi type VI _h cosmological model filled with perfect fluid in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). We have obtained the cosmological models by solving the field equations. Some physical behaviors of the model are also studied.