Constant Ricci Scalar Research Articles

Exact rotating black hole solutions for f(R) gravity by modified Newman Janis algorithm

We show that the f(R)-gravity theories with constant Ricci scalar in the Jordan/Einstein frame can be described by Einstein or Einstein–Maxwell gravity with a cosmological term and a modified gravitational constant. To obtain the rotating axisymmetric solutions for the Einstein/Einstein–Maxwell gravity with a cosmological constant, we also propose a modified Newmann–Janis algorithm which involves the non-complexification of the radial coordinate and a complexification of the polar coordinate. Using the duality between the two gravity theories we show that the stationary or static solutions for the Einstein/Einstein–Maxwell gravity with a cosmological constant will also be the solutions for the dual f(R)-gravity with constant Ricci scalar.

Gravitating Meron-like topological solitons in massive Yang\u2013Mills theory and the Einstein\u2013Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection A=lambda U^{-1}dU, the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of S^3 (or S^2) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for D=4 and D=5. Finally, we comment on possible generalisations.

Energy conditions for a $$(WRS)_4$$ spacetime in F(R)-gravity

The objective of the present paper is to study 4-dimensional weakly Ricci symmetric spacetimes $(WRS)_4$ with non-zero constant Ricci scalar. We prove that such a $(WRS)_4$ satisfying $F(R)$-gravity field equations represents a perfect fluid with vanishing vorticity. Some energy conditions are studied under the current setting to constrain the functional form of $F(R)$. We examine a couple of popular toy models in $F(R)$-gravity, $F(R)=e^{\alpha R}$ where $\alpha$ is constant and $F(R)=R-\beta \tanh(R)$, $\beta$ is a constant. We also find that the equation of state parameter (EoS) in both models supports the universe's accelerating behavior, i.e., $\omega=-1$. According to the recently suggested observations of accelerated expansion, both cases define that the null, weak, and dominant energy conditions justify their requirements while the strong energy conditions violate them.

Stationary Gravitation Field Equation With Constant Ricci Scalar in Four Dimension

The solution for vacuum Einstein field equation for stationary spherical black hole was first published by Kerr. In this paper, the modified Kerr metric that satisfies Einstein’s condition, is considered. Furthermore, the metric can be modified to obtain stationary black hole metric with arbitrary constant Ricci scalar as generalization from Einstein condition. This condition implies a non-zero Einstein field equation and could be interpreted generally as a stationary black hole placed on a non-vacuum curved space-time background. Characterization of the geometry is to analyze singularity of the manifold, including the physical singularity and the formed horizon. The critical condition of the black hole is also considered. Moreover, surface gravity and surface area of the black hole are also calculated for further research.

Weyl invariance in metric f(R) gravity

We aim to derive the most general f(R) gravity theory, including the matter, so that it be Weyl invariant. Making use of the mathematical equivalence of these theories with an type of scalar-tensor theory, and by imposing the Weyl invariance for the pure gravity as well as for the matter sector, we obtain the fundamental equation that restricts the form of V (phi) (and, accordingly, of f(R)) so that the resulting action to be Weyl invariant in the Jordan frame. We show that this action is not other than the so-called dilaton gravity action with one scalar eld,, which eective mass is R and Phi dependent. In the Einstein frame, the action becomes the Einstein-Hilbert action with the Ricci scalar being constant due to that the eective mass of scalar eld in this frame vanish. So, we can assume that the Ricci scalar, in the Einstein frame, is the true Cosmological Constant. Therefore, is not preposterous to guess that, at least mathematically, all Weyl invariant metric f(R) theory in the Jordan frame is equivalent, at classical level, to the Einstein gravity, in the Einstein frame, with a constant Ricci scalar. At quantum level, as it is known, both theories are not equivalent due to the presence of anomalies in one of the frames.

Exact solutions to quadratic gravity

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

Dynamical variables and evolution of the universe

One of the striking feature of inhomogeneous matter distribution under the effects of fourth-order gravity and electromagnetic field have been discussed in this manuscript. We have considered a compact spherical celestial star undergoing expansion due to the presence of higher curvature invariants of [Formula: see text] gravity and imperfect fluid. We have explored the dynamical equations and field equations in [Formula: see text] gravity. An explicit expression have been found for Weyl tensor and material variables under the dark dynamical effects. Using a viable [Formula: see text] model, some dynamical variables have been explored from splitting the Riemann curvature tensor. These dark dynamical variables are also studied for charged dust cloud with and without the constraint of constant Ricci scalar.

Charged Adiabatic LTB Gravitational Collapse in f (R) Gravity

We study evolutionary properties of isotropic charged spherical Lemaitre-Tolman-Bondi fluid undergoing non-adiabatic collapse with general f(R) background. We explore exact analytical models of Maxwell- f(R) field equations with constant Ricci scalar. The dynamics of the collapsing system is investigated through system energy content, cosmological and black hole horizons in the presence of electromagnetic field. It is concluded that in addition to matter variables and f(R) corrections, the charge also affects the time interval between formation of respective horizons and singularities. We also find that f(R) corrections as well as electromagnetic field tend to slow down the collapsing process.

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.

The plane symmetric vacuum solutions of modified field equations in metric f(R) gravity

The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.

Static spherically symmetric solutions in F(R) gravity

A Lagrangian derivation of the Equation of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in $F(R)$-gravity. All known exact solutions are recovered. We also exibit a new non trivial solution with non constant Ricci scalar.

Gravitational perfect fluid collapse in f(R) gravity

In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f(R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f(R 0) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f(R 0) plays the role of the cosmological constant.

A NOTE ON CONSTANT CURVATURE SOLUTIONS IN CYLINDRICALLY SYMMETRIC METRIC f(R) GRAVITY

In the previous work we introduced a new static cylindrically symmetric vacuum solution in Weyl coordinates in the context of the metric f(R) theories of gravity.1 Now we obtain a two-parameter family of exact solutions which contains a cosmological constant and a new parameter as β. This solution corresponds to a constant Ricci scalar. We proved that in f(R) gravity the constant curvature solution in cylindrically symmetric cases is only one member of the most generalized Tian family in GR. We show that our constant curvature exact solution is applicable to the exterior of a string. The sensibility of stability under initial conditions is discussed.

Elastic stars in general relativity: III. Stiff ultrarigid exact solutions

We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass–radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable.

Shear-free, irrotational, geodesic, anisotropic fluid cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form , with , then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.