Comprehensive quasi-Einstein spacetime with application to general relativity

The aim of this paper is to extend the notion of all known quasi-Einstein (QE) manifolds like generalized QE, mixed generalized QE manifold, pseudo generalized QE manifold and many more and name it comprehensive QE manifold [Formula: see text]. We investigate some geometric and physical properties of the comprehensive QE manifolds [Formula: see text] under certain conditions. We study the conformal and conharmonic mappings between [Formula: see text] manifolds. Then we examine the [Formula: see text] with harmonic Weyl tensor. We define the manifold of comprehensive quasi-constant curvature and prove that conformally flat [Formula: see text] is manifold of comprehensive quasi-constant curvature and vice versa. We study the general two viscous fluid spacetime [Formula: see text] and find out some important consequences about [Formula: see text]. We study [Formula: see text] with vanishing space matter tensor. Finally, we prove the existence of such manifolds by constructing nontrivial example.

Wormhole solutions in Rastall gravity theory

This work looks for new wormhole solutions in the non-conservative Rastall gravity. Although Rastall gravity is considered to be a higher-dimensional gravity, the actual diversion from general relativity essentially happens due to a modification in the corresponding matter tensor part. Thus, it would be interesting to find out if such non-minimal coupling has any effect on the traversable wormholes and their corresponding energy conditions.

Characterizations of mixed quasi-Einstein manifolds

The object of the present paper is to study mixed quasi-Einstein manifolds. Some geometric properties of mixed quasi-Einstein manifolds have been studied. We also discuss [Formula: see text] spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a mixed quasi-Einstein spacetime.

A New Class of Almost Ricci Solitons and Their Physical Interpretation

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u,μ,p,α,η,σij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems.

On Pseudo-Petrov Symmetric Riemannian Manifolds

The present paper deals with pseudo-Petrov symmetric Riemannian manifolds whose space-matter tensor satisfies a special condition. Firstly, basic results of pseudo-Petrov symmetric Riemannian manifolds are obtained. Then, pseudo-Petrov symmetric manifolds which are Einstein, quasi-Einstein, and locally decomposable are examined and some theorems involving these manifolds are proved. Finally, two examples proving the existence of pseudo-Petrov symmetric Riemannian manifolds are given.

THE MANY FACES OF THE MASSLESS TENSOR GAUGE FIELD OF DEGREE TWO

Starting from a generic second-order Lagrangian density (that describes the dynamics of an Abelian tensor gauge field of degree two and depends on two arbitrary real constants) we first perform the Dirac analysis. This procedure reveals seven distinct situations (dictated by the values of the real parameters that label the second-order Lagrangian density) in each of them one determines the number of degrees of freedom and also a generating set of gauge transformations. Second, with the help of some auxiliary gauge/matter tensor gauge fields of degree three, in each of the seven situations aforementioned, we construct the first-order Lagrangian density corresponding to the second-order one.

GEOMETRY AND MATTER REDUCTION IN A 5D KALUZA–KLEIN FRAMEWORK

In this paper we consider the Kaluza–Klein field equations in the presence of a generic 5D matter tensor which is governed by a conservation equation due to 5D Bianchi identities. Following a previous work, we provide a consistent approach to matter where the problem of huge massive modes is removed, without relaxing the compactification hypotheses; therefore we perform the dimensional reduction either for metric fields and for matter, thus identifying a pure 4D tensor term, a 4D vector term and a scalar one. Hence we are able to write down a consistent set of equations for the complete dynamics of matter and fields; with respect to the pure Einstein–Maxwell system we now have two additional scalar fields: the usual dilaton one plus a scalar source term. Some significant scenarios involving these terms are discussed and perspectives for cosmological applications are suggested.

DYNAMICS OF MATTER IN A COMPACTIFIED KALUZA–KLEIN MODEL

A long-standing problem in Kaluza–Klein models is the description of matter dynamics. Within the 5D model, the dimensional reduction of the geodesic motion for a 5D free test particle formally restores electrodynamics, but the reduced 4D particle shows a charge–mass ratio that is upper-bounded, such that it cannot fit in with any kind of elementary particle. At the same time, from the quantum dynamics viewpoint, there is the problem of the generation of huge massive modes. We present a criticism against the 5D geodesic approach and face the hypothesis that in Kaluza–Klein space the geodesic motion does not deal with the real dynamics of the test particle. We propose a new approach: starting from the conservation equation for the 5D matter tensor, within the Papapetrou multipole expansion, we prove that the 5D dynamical equation differs from the 5D geodesic one. Our new equation provides right coupling terms without bounding and in such a scheme the tower of massive modes is removed.