Instability ranges of collapsing star through adiabatic index in f(T, Θ) theory of gravity

The main purpose of this paper is to study the stability analysis of collapsing star in the scenario of Newtonian and post Newtonian approximations. We consider the cylindrical symmetry of collapsing object which is filled with anisotropic fluid. The f(T, Θ) theory of gravity, where T is the torsion scalar and Θ is the trace of energy-momentum tensor is taken into account. The dynamical field equations are constructed which help to derive collapse equation by applying the perturbation method. The stability behavior of collapsing star is defined in both Newtonian and post Newtonian approximations with the help of an adiabatic index.     

Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.     

Effects of charge on gravitational decoupled anisotropic solutions in f(R) gravity

This paper is devoted to studying charged anisotropic static spherically symmetric solutions through gravitationally decoupled minimal geometric deformation technique in f(R) gravity. For this purpose, we first consider the known isotropic Krori–Barua solution for f(R) Starobinsky model in the interior of a charged stellar system and then include the effects of two types of anisotropic solutions. The corresponding field equations are constructed and the unknown constants are obtained from junction conditions. We analyze the physical viability and stability of the resulting solutions through effective energy density, effective radial/tangential pressure, energy conditions, and causality condition. It is found that both solutions satisfy the stability range as well as other physical conditions for specific values of charge as well as model parameter and anisotropic constant. We conclude that the modified theory under the influence of charge yields more stable behavior of the self-gravitating system.     

Effects of charge on dynamical instability of spherical collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The effects of charge on stable structure of spherically symmetric collapsing model comprising anisotropic matter distribution are studied in f(R, T) gravity, where R and T correspond to scalar curvature and trace of the energy-momentum tensor, respectively. We construct the field equations, Maxwell equations and dynamical equations in this scenario. We employ linear perturbation scheme on physical variables, metric functions as well as modified terms to establish the evolution or collapse equation for a consistent functional form of f(R, T) gravity. We investigate the limit of instability in Newtonian as well as post Newtonian regimes. It is found that charge plays a fundamental role to slow down the collapse and form a more stable system.     

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.     

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.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Graviton and scalar propagations on AdS<Subscript>4</Subscript> space in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravities

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents

In this paper, the metric approach of f(R) theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f(R) gravity for some appropriate f(R) model, which turns out to be a constant quantity.     

Testing gravity with non-Gaussianity

We show that modified gravity presents distinctive nonlinear features on the Cosmic Microwave Background (CMB) anisotropies comparing with General Relativity (GR). We calculate the contribution to the CMB non-Gaussianity from nonlinear Sachs-Wolfe effect in f(R) gravity and show that, contrary to GR?s contribution which is typically ?O(1), the contribution in f(R) gravity is sensitive to the nonlinear structure of f(R) and can be large in principle. Optimistically, this gives an alternative origin for the possibly observed large CMB non-Gaussianities besides the primordial ones. On the other hand, such nonlinear features can be employed to provide a new cosmological test of f(R) or other modified theories of gravitation, which is unique and independent of previously known tests.     

Thermal fluctuations of dyadosphere of Reissner-Nordström,Janis-Newman-Winicour and f(R) global monopole black holes

In this paper, we study the effects of thermal fluctuations on Dyadosphere of Reissner-Nordström, Janis-Newman-Winicour and the fragmentation of f(R) global monopole black holes. In the presence of these fluctuations, we obtain various thermodynamic quantities like pressure, entropy, specific heat, Canonical and Grand Canonical ensembles. We discuss the stability of these black holes using the γ (the ratio of heat capacities). We also discuss the phase transition and range of local and global stability. It is demonstrated that in Dyadoshpere of Reissner-Nordström, Janis-Newman-Winicour and fragmentation of f(R) global monopole black holes become locally and globally stable due to logarithmic correction term and large horizon radius.     

Lanczos-Lovelock and f(R) Gravity from Clifford Space Geometry

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the generalized connections in Clifford spaces (C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f(R),f(R _μν ),… actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D>4 play an important role in finding specific examples.     

Future cosmological evolution in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity using two equations of state parameters

We investigate the issues of future oscillations around the phantom divide (FOPD) for f(R) gravity. For this purpose, we introduce two types of energy density and pressure arisen from the f(R)-higher order curvature terms. One has the conventional energy density and pressure even in the beginning of the Jordan frame, whose continuity equation defines the native equation of state w _DE. On the other hand, the other has the different energy density and pressure which do not obviously satisfy the continuity equation. This needs to introduce the effective equation of state w _eff to describe the f(R)-fluid, in addition to the native equation of state [(w)\tilde]_DE\tilde{w}_{\mathrm{DE}}. We show that the FOPD occur in f(R) gravities by introducing two types of equation of state. Finally, we point out that the singularity appears ar x=x _c because the stability condition of f(R) gravity violates.     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.     

Bianchi Type-V Cosmology in f(R,T) Gravity with Λ(T)

A new class of cosmological models in f(R,T) modified theories of gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T, have been investigated for a specific choice of f(R,T)=f ₁(R)+f ₂(T) by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$ , where n and α are positive constants. For 0<n≤1, this generates a class of accelerating models while for n>1, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct f(R,T) models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant Λ as a function of the trace of the stress energy-momentum-tensor, and dub such a model “Λ(T) gravity” where we have specified a certain form of Λ(T). Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair {r,s} parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.