Perfect Fluid Spacetimes Research Articles

Perfect fluid spacetimes and Yamabe solitons

This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid spacetime is Ricci recurrent if and only if the velocity vector field of perfect fluid spacetime is parallel and α = β. In addition, in a stiff matter perfect fluid Yang pure space with p + σ ≠ 0, the integral curves generated by the velocity vector field are geodesics. Moreover, it is shown that in a generalized Robertson–Walker perfect fluid spacetime, the Weyl tensor is divergence-free and the gradient of the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime. We also characterize the perfect fluid spacetimes whose Lorentzian metrics are Yamabe and gradient Yamabe solitons, respectively.

Hyper generalized pseudo Q-symmetric semi-Riemannian manifolds

The object of the present paper is to study the properties of a hyper generalized pseudo \(Q\)-symmetric semi-Riemannian manifold, proving that under certain assumptions, it is a perfect fluid spacetime.

P1-Curvature tensor in the space time of general relativity

The P1 - curvature tensor defined from W3 - curvature tensor has been studied in the space time of general relativity. The Bianchi like differential identity is satisfied by P1 - tensor if and only if the Ricci tensor is of Codazzi type. It is shown that Einstein like field equations can be expressed with the help of the contracted part of P1 - tensor, which is conserved if the energy momentum tensor is Codazzi type. Considering P1 -flat space time satisfying Einstein’s field equations with cosmological term, the existence of Killing vector field ξ is shown if and only if the Lie derivative of the energy-momentum tensor vanishes with respect to ξ, as well as admitting a conformal Killing vector field is established if and only if the energy-momentum tensor has the symmetry inheritance property. Finally for a P1 - flat perfect fluid space time satisfying Einstein’s equations with cosmological term, some results are obtained.

Almost pseudo-Ricci symmetric spacetime solutions in F(R)-gravity

The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $$(\textit{APRS})_4$$ . We show that a Robertson–Walker spacetime is $$(\textit{APRS})_4$$ and vice versa under certain condition imposed on its scale factor. Some popular toy models of F(R)-gravity are also studied under the current setting and various energy conditions are investigated.

Characterization of perfect fluid spacetimes admitting gradient [formula omitted]-Ricci and gradient Einstein solitons

We set the goal to study the properties of perfect fluid spacetimes endowed with the gradient η-Ricci and gradient Einstein solitons.

Curvature properties of Kantowski–Sachs metric

In this paper we have investigated the curvature restricted geometric properties of the generalized Kantowski–Sachs (briefly, GK–S) spacetime metric, a warped product of 2-dimensional base and 2-dimensional fibre. It is proved that GK–S metric describes a generalized Roter type, 2-quasi Einstein and Ein(3) manifold. It also has pseudosymmetric Weyl conformal tensor as well as conharmonic tensor and its conformal 2-forms are recurrent. Further, it realizes the curvature condition R⋅R=Q(S,R)+L(t,θ)Q(g,C) (see, Theorem 4.1). We have also determined the curvature properties of Kantowski–Sachs (briefly, K–S), Bianchi type-III and Bianchi type-I metrics which are the special cases of GK–S spacetime metric. The sufficient condition under which GK–S metric represents a perfect fluid spacetime has also been obtained.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

On generalized projective [formula omitted]-curvature tensor

The object of the present paper is to introduce and investigate the P-curvature tensor that generalizes projective, conharmonic, M-projective and the set of Wi curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P-curvature tensor are Einstein and those admitting flat P-curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P-curvature tensor are given in each subspace of Gray’s decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P-curvature tensor or a divergence free P-curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P-curvature tensor are considered.

Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the [Formula: see text] gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the [Formula: see text] gravity.

Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime

In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.

A note on classification of static plane symmetric perfect fluid space-times via proper conformal vector fields in f(G) theory of gravity

In the [Formula: see text] theory of gravity, we classify static plane symmetric perfect fluid space-times via proper conformal vector fields (CVFs) using algebraic and direct integration approaches. During this classification, we found eight cases. Studying each case in detail, we found that the dimensions of CVFs are 4, 5, 6 or 15. In the cases when the space-time admits 15 independent CVFs it becomes conformally flat.

On harmonicity and Miao–Tam critical metrics in a perfect fluid spacetime

The curvature properties of a perfect fluid spacetime have been studied when the Riemann curvature, the projective curvature, the concircular curvature, the conformal curvature and the conharmonic curvature tensors are, respectively, harmonic. In the flatness case, if the velocity vector of the fluid is torse-forming, we can completely characterize it. Also, we study the consequences of the existence of $$\eta $$ -Einstein, $$\eta $$ -Ricci and $$\eta $$ -Yamabe solitons in perfect fluid spacetime satisfying Miao–Tam critical metric condition.

Spacetimes with different forms of energy–momentum tensor

The object of the present paper is to characterize spacetimes with different types of energy–momentum tensor. At first we consider spacetimes with pseudo symmetric energy–momentum tensor T. We obtain a necessary and sufficient condition for a spacetime with pseudo symmetric energy–momentum tensor to be a pseudo Ricci symmetric spacetime. Next we consider the spacetimes with Codazzi type of energy–momentum tensor and several interesting results are pointed out. Moreover, some results related to perfect fluid spacetimes with different forms of energy–momentum tensors have been obtained. We study spacetimes with quadratic Killing energy–momentum tensor T and show that a GRW spacetime with quadratic Killing energy–momentum tensor is an Einstein space. Finally, we have considered general relativistic spacetimes with semisymmetric energy–momentum tensor and obtained some important results.

Solitons and geometrical structures in a perfect fluid spacetime

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and η-Ricci and η-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field ξ of the soliton is of gradient type, ξ:= grad(f), we derive a Poisson equation from the soliton equation.

Harmonic Aspects in an $\eta$-Ricci Soliton

We characterize the $\eta$-Ricci solitons $(g,\xi,\lambda,\mu)$ for the special cases when the $1$-form $\eta$, which is the $g$-dual of $\xi$, is a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $\eta$ to be a solution of the Schr\"{o}dinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner-Weitzenb\"{o}ck techniques, we formulate some more conclusions for the case of gradient solitons and deduce topological properties of the manifold and its universal covering.

The Kiselev black hole is neither perfect fluid, nor is it quintessence

The Kiselev black hole spacetime is an extremely popular toy model, with over 200 direct and indirect citations as of 2019. Unfortunately, despite repeated assertions to the contrary, this is not a perfect fluid spacetime. The relative pressure anisotropy and average pressure are easily calculated, and the relative pressure anisotropy is generally non-zero, (except for the special case where Kiselev’s model degenerates to Schwarzschild-(anti)–de Sitter spacetime). Kiselev’s original paper was very careful to point this out in the calculation, but then in the discussion made a somewhat unfortunate choice of terminology which has (with very limited exceptions) been copied into the subsequent literature. Perhaps worse, Kiselev’s use of the word ‘quintessence’ does not match the standard usage in the cosmology community, leading to another level of unfortunate and unnecessary confusion. Very few of the subsequent follow-up papers get these points right, so a brief explicit comment is warranted.

Decomposition of the total stress energy for the generalized Kiselev black hole

We demonstrate that the anisotropic stress-energy supporting the Kiselev black hole can be mimicked by being split into a perfect fluid component plus either an electromagnetic component or a scalar field component, thereby quantifying the precise extent to which the Kiselev black hole fails to represent a perfect fluid spacetime. The perfect fluid component carries either an electric or a scalar charge, which then generates anisotropic electromagnetic or scalar fields. This in turn generates anisotropic contributions to the stress-energy. These in turn induce forces which partially (in addition to the fluid pressure gradient) support the matter content against gravity. This decomposition is carried out both for the original 1-component Kiselev black hole and for the generalized N-component Kiselev black holes. We also comment on the presence of energy condition violations (specifically for the null energy condition --- NEC) for certain sub-classes of Kiselev black holes.

Semiconformal curvature tensor and perfect fluid spacetimes in general relativity

The semiconformal curvature tensor and its divergence have been studied for perfect fluid spacetimes. It is seen, apart from other results, that the perfect fluid spacetimes with divergence-free semiconformal curvature tensor either satisfy the vacuum-like equation of state or represent FLRW cosmological model.

On pseudo H-symmetric Lorentzian manifolds with applications to relativity

In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of the manifold vanishes and conversely. Moreover, we deal with pseudo H-symmetric perfect fluid spacetimes and obtain several interesting results. Also, we present some results of the spacetime satisfying divergence free H-curvature tensor. Finally, we construct a non-trivial Lorentzian metric of (PHS)4.

Static perfect fluid space-time on compact manifolds

The purpose of this article is to investigate the geometry of static perfect fluid space-time metrics on compact manifolds with boundary. In the first part, we provide a boundary estimate for static perfect fluid space-time. In the second part, we establish a unified Böchner type formula for a large class of spaces that include the static perfect fluid space-time, critical metrics of the volume functional, static spaces and CPE metrics. Moreover, as a consequence of such a formula we obtain a gap result for a compact static perfect fluid space-time.