Dust Static Cylindrically Symmetric Solutions in f(R) Gravity

This paper is devoted to investigate non-vacuum solutions of cylindrically symmetric spacetime in the context of metric f(R) gravity. We take dust matter to find energy density of the universe. In particular, we find two exact solutions, which correspond to two f(R) models in each case. The first solution provides constant curvature while the second solution corresponds to non-constant curvature. The functions of the Ricci scalar and energy densities are evaluated in each case.     

Dust Static Cylindrically Symmetric Solutions in f(R) Gravity

This paper is devoted to investigate non-vacuum solutions of cylindrically symmetric spacetime in the context of metric f(R) gravity. We take dust matter to find energy density of the universe. In particular, we find two exact solutions, which correspond to two f(R) models in each case. The first solution provides constant curvature while the second solution corresponds to non-constant curvature. The functions of the Ricci scalar and energy densities are evaluated in each case.     

Energy Distribution for a Power Model of the Plane Symmetric Spacetime in f(R) Gravity

The study of the energy localization in f(R) theories of gravity has attracted much interest in recent years. In this paper, the vacuum solutions of the modified field equations for a power model of plane symmetric metric are studied in metric f(R) gravity with the assumption of constant Ricci scalar. Next, we determine the energy-momentum complexes in f(R) theories of gravity for this spacetime for some important models. We also show that these models satisfy the stability and constant curvature conditions.     

Energy Distribution for a Power Model of the Plane Symmetric Spacetime in f (R) Gravity

The study of the energy localization in f(R)theories of gravity has attracted much interest in recent years.In this paper,the vacuum solutions of the modified field equations for a power model of plane symmetric metric are studied in metric f(R)gravity with the assumption of constant Ricci scalar.Next,we determine the energy-momentum complexes in f(R)theories of gravity for this spacetime for some important models.We also show that these models satisfy the stability and constant curvature conditions.     

Renormalization aspects of \mathcal {N}=1 Super Yang–Mills theory in the Wess–Zumino gauge

The generalized $f(R)$ gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho $ , we not only discuss the constraints on the model parameters $m,n$ , but also illustrate the evolutionary trajectories of the scale factor $a(t)$ , the deceleration parameter $q(t)$ , and the scalar field $\epsilon (t),\phi (t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.     

Energy Bounds for Static Spherically Symmetric Spacetime in f(R,G) Gravity

The main purpose of this paper is to investigate energy bounds in the context of f(R,G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R,G) gravity to develop the field equations. We select three different models of f(R,G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R,G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.     

Energy Bounds for Static Spherically Symmetric Spacetime in f(R,G) Gravity

The main purpose of this paper is to investigate energy bounds in the context of f(R, G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R, G) gravity to develop the field equations. We select three different models of f(R, G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R, G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.     

Cosmological analysis of scalar field models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper determines the existence of Noether symmetry in non-minimally coupled f(R, T) gravity admitting minimal coupling with scalar field models. We consider a generalized spacetime which corresponds to different anisotropic and homogeneous universe models. We formulate symmetry generators along with conserved quantities through Noether symmetry technique for direct and indirect curvature–matter coupling. For dust and perfect fluids, we evaluate exact solutions and construct their cosmological analysis through some cosmological parameters. We conclude that decelerated expansion is obtained for the quintessence model with a dust distribution, while a perfect fluid with dominating potential energy over kinetic energy leads to the current cosmic expansion for both phantom as well as quintessence models.     

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Exact calculation of O(α) QED corrections for f_1 \overline {f_1 } \uparrow f_2 \overline {f_2 } processes induced by polarized incident particles

For $f_1 \overline {f_1 } \uparrow f_2 \overline {f_2 }$ (γ) processes induced by polarized incident particles, exact covariant expressions for the energy spectrum of one of the emitted fermions, for the total cross section, and for the polarization asymmetry are obtained in theα³ order of QED.     

A GROUP OF EXACT (3+1) DIMENSIONAL CYLINDRICALLY SYMMETRIC WAVE SOLUTIONS TO THE EINSTEIN GRAVITATIONAL FIELD EQUATION

Starting with the diagonal spacetime metric tensor, the Einstein gravitational field equation is solved, and a set of exact (3+1) dimensional cylindrically symmetric wave solutions with two arbitrary functions are found. In these solutions all nonvanishing components of spacetime metric tensor are varying with the same propagating factor (ct-z) while the waves are travelling along z axis. The physical picture and the condition of positive energy density of the wave solutions are discussed.     

Behavior of Anisotropic Compact Stars in f(R, ?) Gravity

The aim of this paper is to investigate modified f(R, ?) theory of gravity, where R and ? represent the Ricci scalar and scalar potential respectively. Specifically, we take the spherically symmetric spacetime to discuss the possible emergence of compact stars. We study the physical behavior of compact stars by considering 4 U 1820-30, SAX J1808-3658 and Her X1, which are three popular models of compact stars. The graphical analysis of energy density, radial pressure, tangential pressure, energy conditions as well as stability of compact stars has been shown. It is concluded that behavior of these three stars is usual for f(R, ?) gravity models with some specific choices of model parameters.     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Exact anyon black hole solutions

We present the exact anyon solutions and study their energy conditions. It is shown that the exact anyon VdW solutions with \(b>0\) are physically un-acceptable. Especially for the reduced case \(b=0\), after carefully studying its energy conditions, geometric quantities and horizon structure, we conclude that there is an anyon black hole taking the precisely same thermodynamical phase space with the gas of “interacting point particle” (IPP), which should exhibit a quasi Fermi–Dirac statistics and have an upper bound of mass. The anyon IPP black hole can contain 1 or 2 horizons. This is the first physical VdW-like black hole solution in the global spacetime. Moreover, there exist the Hawking-Page phase transition between the anyon IPP black holes and the pure thermal radiation phase.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.     

Dynamical wormhole solutions in f(T) gravity

We study dynamical wormhole solutions in the framework of $f(T)$ f ( T ) theory of gravity with anisotropic fluid. We assume a general dynamical spherically symmetric wormhole spacetime with specific form of the shape function and scale factor. The scale factor is taken in the power-law form in order to meet the accelerated expansion of the universe. We discuss the behavior of energy conditions for three particular choices of equation of state, i.e., radial and transverse pressures in linear form with energy density and traceless fluid. The energy conditions satisfy for certain time intervals in all cases. The radial coordinate does not play any role in graphs and the validity or violation of energy conditions depend upon the time coordinate only. The graphical behavior of the energy conditions become equivalent for radial and transverse pressures in all the three cases.     

C-Field Cosmology in Higher Dimensions

Hoyle and Narlikar's C-field cosmology is extended in the framework of higher dimensional spacetime and a class of exact solutions is obtained. Adjusting the arbitrary constants of integration one can show that our model is amenable to the desirable property of dimensional reduction so that the universe ends up in an effective 4D one. Further with matter creation from the C-field the mass density steadies with time and the usual bigbang singularity is avoided. An alternative mechanism is also suggested which seems to provide matter creation in the 4D spacetime although total matter in the 5D world remains conserved. Quintessence phenomenon and energy conditions are also discussed and it is found that in line with the physical requirements our model admits a solution with a decelerating phase in the early era followed by an accelerated expansion later. Moreover, as the contribution from the C-field is made negligible a class of our solutions reduces to the previously known higher dimensional models in the framework of Einstein's theory.     

<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.     

Exact traveling wave solutions to nonlinear diffusion and wave equations

By the introduction of some ansatz equations, we have obtained several new classes of traveling (solitary) wave solutions to the nonlinear diffusion equation $$f_1 (u)u_t + f_2 (u)u_x + f_3 (u)u_{xx} + f_4 (u)u_x^2 = f_5 (u)$$ and the nonlinear wave equation $$f_1 (u)u_u + f_2 (u)u_t + f_3 (u)u_{xx} + f_4 (u)u_x + f_5 (u)u_x^2 + \cdots = f_6 (u)$$ Some applications of these solutions are discussed.