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.     

Plane Symmetric Solutions in f(R,T) Gravity

The main purpose of this paper is to investigate the exact solutions of plane symmetric spacetime in the context of f(R,T)gravity[Phys.Rev.D 84(2011)024020],where f(R,T)is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T.We explore the exact solutions for two different classes of f(R,T)models.The first class f(R,T)=R+2f(T)yields a solution which corresponds to Taub's metric while the second class f(R,T)=f_1(R)+f_2(T)provides two additional solutions which include the well known anti-deSitter spacetime.The energy densities and corresponding functions for f(R,T)models are evaluated in each case.     

Conformal Continuations in Gravitation Theory with Lagrangian <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)

Static spherically-symmetric vacuum solutions of gravitation theory equations with Lagrangian f(R) are examined, where R is a scalar curvature and f is an arbitrary function. Equations of f(R)-theories are reduced to the Einstein scenario — general relativity theory (GRT) equations with a source in the form of a scalar field with potential — with the use of the well-known conformal transformation. The necessary and sufficient conditions of existence of solutions admitting conformal continuations are formulated. This means that the central singularity of the Einstein scenario is mapped into a regular sphere S_trans of the Jordan scenario (that is, into the manifold corresponding to the initial formulation of the theory), and a solution of the field equations can be smoothly continued through it. The value of curvature R on the sphere S_trans corresponds to an extremum of the function f(R). Concrete examples are considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–51, September, 2005.     

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.     

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.     

Quantum Cosmology in Higher Derivative and Scalar-Tensor Gravity

The Bicknell theorem states that a non-linear Lagrangian can be recast in the form of a scalar-tensor theory, with a suitable potential, through a conformal transformation. In this paper, we first show that such classical equivalence remains valid at the level of the Wheeler—deWitt equation. Then, we consider a specific case, represented by a Lagrangian f(R) = R + l^–2(l²R)^4/3 whose vacuum cosmological solutions describe a non-singular Universe. The corresponding scalar-tensor theory and its cosmological solutions are written down. We find again non-singular solutions. The Wheeler—deWitt equation for this case is analyzed. The application of the Bicknell theorem leads to the interpretation of the behaviour of the scale factor in terms of the matter content, represented by the scalar field, and consequently to the energy conditions. The problem of classical and quantum regime is discussed and the classical behaviour is recovered, from the quantum solutions, near the maximum of the scale factor where the strong energy condition is satisfied.     

Exploding spheres of dust

In this paper, we extend the work of Oppenheimer & Snyder (1939) who treated the zero curvature case in the gravitational collapse of spheres of dust intended to represent collapsing stars. A solution is given which is valid for all space and is characterized by negative curvature of the space within a sphere of dust. This solution is obtained by matching the negative curvature interior solution (as well as, for completeness, zero and positive curvatures interior solutions) to an exterior Schwarzschild geometry. In this solution, corresponding to the case of a Newtonian system with positive total energy, the mass as seen by an observer at infinity is found to be positive definite. Also, in each case, the positive definite massm is related to the density and radiusr [defined as the square root of the (surface area/4)] of the dust cloud viam=(4/3)pr ³. The methods employed here for matching interior and exterior solutions are applicable to the construction of cosmological models in which the sign of the curvature and/or expansion rate differ in two or more regions, e.g. a universe expanding in one region and contracting in another.     

Quadratic metric‐affine gravity

We consider spacetime to be a connected real 4‐manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is (purely) quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we look for Riemannian solutions, i.e. solutions whose connection is Levi‐Civita. We find two classes of Riemannian solutions: 1) Einstein spaces, and 2) spacetimes with pp‐wave metric of parallel Ricci curvature. We prove that for a generic quadratic action these are the only Riemannian solutions. In the second part of the paper we look for non‐Riemannian solutions. We define the notion of a “Weyl pseudoinstanton” (metric compatible spacetime whose curvature is purely of Weyl type) and prove that a Weyl pseudoinstanton is a solution of our field equations. Using the pseudoinstanton approach we construct explicitly a non‐Riemannian solution which is a wave of torsion in a spacetime with Minkowski metric. We discuss the possibility of using this non‐Riemannian solution as a mathematical model for the neutrino.     

Two-Flux Colliding Plane Waves in String Theory

We construct the two-flux colliding plane wave solutions in higher-dimensional gravity theory with dilaton,and two complementary fluxes. Two kinds of solutions have been obtained: Bell-Szekeres (BS) type and homogeneous type. After imposing the junction condition, we find that only the BS type solution is physically well-defined. Furthermore, we show that the future curvature singularity is always developed for our solutions.     

Uniqueness and nonuniqueness in the Einstein constraints

The conformal thin-sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find two distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with nonunique solutions is also of broader interest.     

The Lynden-Bell and Katz definition of gravitational energy: Applications to singular solutions

We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and spherically symmetric space-times which admit a curvature singularity. These are the Tolman V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th of the gravitational radius. We show that the LK definition can still be applied to these solutions despite the presence of a singularity which nonetheless appears to carry no energy in the LK sense. While in the solutions that we mentioned the KL gravitational energy is positive definite everywhere in space time, this is not the case for the overcharged Reissner-Nordström space-time. In the latter case in fact the LK energy density becomes negative sufficiently close to the singularity hence we use the positivity criterion to impose a more stringent limit of validity to the Reissner-Nordström solution.     

Plausible black hole solutions in higher-derivative gravity

Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants.     

Non-Einsteinian gravitational Lagrangians assuring cosmological solutions without collapse

We discuss a method of determining the form of the hypothetical gravitational Lagrangianf(R) replacing the Einsteinian LagrangianR in order to avoid the singularity in cosmological solutions. Instead of supposing some form off(R) and then trying to solve the generalized Einstein equations, we treatf(R) as an unknown function while inserting the cosmological solution coinciding with Friedmann solution everywhere except for the singularity, which is replaced by a regular minimum of the scale factora (t) (a regular maximum of curvature). Then we findf(R) by numerical integration. The Lagrangians thus obtained for different cases (k=0, ± 1, and with the equation of state corresponding to pure radiation) have some common properties, among which ¦f(R)¦ < ¦R¦ (concavity), and the absence of asymptotes.     

Singularity problem with f(R) models for dark energy

In this Letter, I point out that there is a curvature singularity problem appearing on the nonlinear level that generally plagues f(R) models that modify Einstein gravity in the infrared. It is caused by the fact that for the effective scalar degree of freedom, the curvature singularity is at a finite field value and energy level, and can be easily accessed by the field dynamics in the presence of matter. This problem is invisible in a linearized analysis, except for the telltale growing oscillatory modes it causes. In view of this, the viability of many f(R) models in the current literature will have to be reevaluated.     

A New Exponential Gravity

We propose a new exponential f（R） gravity model with f（R） = （R - λc） e^λ（c/R）n and n 〉 3, λ ≥ 1, c 〉 0 to explain late-time acceleration of the universe. At the high curvature region, the model behaves like the A CDM model. In the asymptotic future, it reaches a stable de-Sitter spaeetime. It is a cosmologically viable model and can evade the local gravity constraints easily. This model shares many features with other f（R） dark energy models like Hu-Sawicki model and ExponentiM gravity model. In it the dark energy equation of state is of an oscillating form and can cross phantom divide line ωde = -1. In particular, in the parameter range 3 〈 n ≤ 4, λ ～ 1, the model is most distinguishable from other models. For instance, when n = 4, λ = 1, the dark energy equation of state will cross -1 in the earlier future and has a stronger oscillating form than the other models, the dark energy density in asymptotical future is smaller than the one in the high curvature region. This new model can evade the local gravity tests easily when n 〉 3 and λ 〉 1.     

Dirac Quasinormal Modes of Static f(R) de Sitter Black Holes

Quasinormal modes(QNMs) for Dirac perturbations of f(R) black holes(BHs) are described in this paper,involving two types of f(R) solution: f(R)(Schwarzschild) BHs and f(R)(Maxwell) BHs. With the finite difference method, the stability of the f(R) black holes(BHs) is analysed and the threshold range of f(R)(Schwarzschild) BHs and f(R)(Maxwell) BHs is defined respectively. The results show that due to the presence of the correction factor R0, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values |k| on the f(R) BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with|k| increasing. Furthermore, under the Dirac perturbation, the stability of f(R) solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters(|k|, charge Q and mass m) are discussed in massless, and massive cases, by contrast to the classical BHs.     

Gravity and large black holes in Randall-Sundrum II braneworlds

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ?. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20?. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution.     

De Sitter solutions in higher order gravity

We consider de Sitter solutions, relevant for instance in studies of inflation, in cosmologies where the gravitational Lagrangian is a functionf(R),R being the scalar curvature. Previous investigations have mostly concentrated onf(R) = R+R² which always has a solution matching the conventional de Sitter one. We show that this circumstance is rather exceptional, and that one must go to higher terms to see signs of the generic behaviour, In general the de Sitter solutions are different from those of Einstein gravity. We present complete solutions for the general cubic Lagrangian. We also address the question of when the solutions to equations from truncated actions can be expected to well represent solutions of some full (and possibly unknown) theory. Such theories provide the possibility of weakening the bounds on the energy density of the inflaton, allowing an easier reconciliation of the inflationary universe with structure-forming topological defects.