scholarly journals General properties of f(R) gravity vacuum solutions

2020 ◽  
Vol 29 (13) ◽  
pp. 2050089
Author(s):  
Salvatore Capozziello ◽  
Carlo Alberto Mantica ◽  
Luca Guido Molinari
Keyword(s):  
Weyl Tensor ◽  
Ricci Tensor ◽  
Curvature Scalar ◽  
General Properties ◽  
Walker Metric ◽  
Vacuum Solutions

General properties of vacuum solutions of [Formula: see text] gravity are obtained by the condition that the divergence of the Weyl tensor is zero and [Formula: see text]. Specifically, a theorem states that the gradient of the curvature scalar, [Formula: see text], is an eigenvector of the Ricci tensor and, if it is timelike, the spacetime is a Generalized Friedman–Robertson–Walker metric; in dimension four, it is Friedman–Robertson–Walker.

scholarly journals Conformal gravity and “gravitational bubbles”

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641004 ◽  
Author(s):  
V. A. Berezin ◽  
V. I. Dokuchaev ◽  
Yu. N. Eroshenko
Keyword(s):  
General Structure ◽  
Momentum Tensor ◽  
Curvature Scalar ◽  
Conformal Gravity ◽  
Curved Space ◽  
Material Sources ◽  
Complete Set ◽  
The One ◽  
Vacuum Solutions ◽  
The Universe

We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson–Walker metrics. We called one of them the “gravitational bubbles”, which is compact and with zero Weyl tensor. These “gravitational bubbles” are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from “nothing”. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We describe the general structure of the energy-momentum tensor in the spherical conformal gravity and construct the vectorial equation that reveals clearly some features of non-vacuum solutions.

scholarly journals WEYL COLLINEATIONS THAT ARE NOT CURVATURE COLLINEATIONS

2005 ◽  
Vol 14 (08) ◽  
pp. 1431-1437 ◽  
Author(s):  
IBRAR HUSSAIN ◽  
ASGHAR QADIR ◽  
K. SAIFULLAH
Keyword(s):  
Linear Combination ◽  
Lie Algebra ◽  
Curvature Tensor ◽  
Weyl Tensor ◽  
Ricci Tensor ◽  
Lie Symmetries ◽  
Ricci Scalar ◽  
Finite Dimensional ◽  
Fundamental Reason ◽  
Curvature Collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel." Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality."

scholarly journals Cosmological perfect fluids in Gauss–Bonnet gravity

2019 ◽  
Vol 16 (09) ◽  
pp. 1950133 ◽  
Author(s):  
Salvatore Capozziello ◽  
Carlo Alberto Mantica ◽  
Luca Guido Molinari
Keyword(s):  
Perfect Fluid ◽  
Topological Invariant ◽  
Energy Tensor ◽  
Curvature Scalar ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy ◽  
Walker Metric ◽  
Friedmann Robertson Walker ◽  
Hubble Flow

In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.

scholarly journals Weyl compatible tensors

2014 ◽  
Vol 11 (08) ◽  
pp. 1450070 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Luca Guido Molinari
Keyword(s):  
General Relativity ◽  
Constant Curvature ◽  
Weyl Tensor ◽  
Ricci Tensor ◽  
Algebraic Property ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Symmetric Tensors ◽  
Magnetic Part ◽  
Necessary And Sufficient

We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particular, it is shown that the existence of a Weyl compatible vector implies that the Weyl tensor is algebraically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdziński and Shen [11], Hall [15]) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes conditions that were investigated in the literature of general relativity (as in McIntosh et al. [16, 17]). A simple example of Weyl compatible tensor is the Ricci tensor of an hypersurface in a manifold with constant curvature.

scholarly journals On conformally recurrent manifolds of dimension greater than 4

2016 ◽  
Vol 13 (05) ◽  
pp. 1650053
Author(s):  
Carlo Alberto Mantica ◽  
Luca Guido Molinari
Keyword(s):  
Explicit Expression ◽  
Riemannian Manifolds ◽  
Weyl Tensor ◽  
Ricci Tensor ◽  
Symmetric Tensor ◽  
Scalar Function ◽  
Dimension Formula ◽  
Null Recurrence ◽  
Conformally Recurrent

Conformally recurrent pseudo-Riemannian manifolds of dimension [Formula: see text] are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is non-zero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel–Debever–Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.

scholarly journals Derivative couplings in gravitational production in the early universe

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Daniel E. Borrajo Gutiérrez ◽  
Jose A.R. Cembranos ◽  
Luis J. Garay ◽  
Jose M. Sánchez Velázquez
Keyword(s):  
Early Universe ◽  
Ricci Tensor ◽  
Particle Production ◽  
Kinetic Term ◽  
Curvature Scalar ◽  
De Sitter ◽  
Goldstone Bosons ◽  
Highly Sensitive ◽  
Perturbative Regime ◽  
Background Curvature

Abstract Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term. The most general first order action contains derivative couplings to the curvature scalar and to the traceless Ricci tensor, which can be dominant in the case of (pseudo-)Nambu-Goldstone bosons or disformal scalars, such as branons. In the presence of these derivative couplings, the density of produced particles for the adiabatic regime in the de Sitter phase (which mimics inflation) is constant in time and decays with the inverse effective mass (which in turn depends on the coupling to the curvature scalar). In the reheating phase following inflation, the presence of derivative couplings to the background curvature modifies in a nontrivial way the gravitational production even in the perturbative regime. We also show that the two couplings — to the curvature scalar and to the traceless Ricci tensor — are drastically different, specially for large masses. In this regime, the production becomes highly sensitive to the former coupling while it becomes independent of the latter.

Sign in / Sign up

Export Citation Format

Share Document