Perfect Fluid Spacetimes Research Articles

Investigation of space-times through W2-curvature tensor in [formula omitted] gravity

The W2-curvature tensor is an important geometric invariant with relativistic significance, introduced in the early 1970s by Pokhariyal and Mishra, which can be identified in class 4 in the classification of skew-symmetric operators. In this work, we investigate 4-dimensional space-times admitting W2-curvature tensor in f(R,G) modified theory of gravity. It is proved that the W2-curvature flat perfect fluid space-times obeying f(R,G) gravity represent inflation. Also, it is shown that the isotropic pressure and the energy density of such space-times are constant. It is to be noted that in such space-times the considered energy conditions are consistently satisfied if the scalar curvature is positive. Next, we study perfect fluid space-times admitting divergence free W2-curvature tensor in f(R,G) gravity. Amongst other results, we prove that if the energy-momentum tensor of such space-times is bi-recurrent, then either the space-times represent inflation or their isotropic pressure and energy density are constants.

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. Perfect fluids

In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D 104, 064040 (2021); J. Math. Phys. 64, 022501 (2023); J. Math. Phys. 64, 032501 (2023); J. Math. Phys. 64, 042501 (2023); and J. Math. Phys. 64, 052502 (2023)]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed.

Effect of [formula omitted]-curvature tensor in spacetimes and [formula omitted]-gravity

First, we prove that a Lorentzian manifold is of constant curvature if and only if W2-curvature tensor vanishes. We investigate W2-flat perfect fluid spacetime as a solution of fG-gravity theory and we obtain a relation among deceleration, jerk, and snap parameters in a W2-flat spacetime using Friedmann–Robertson–Walker metric. Several energy conditions in terms of Ricci scalar are investigated with the models fG=a1Gn+b1a2Gn+b2 and fG=log(αGn+βe−Gα). For these models, the weak, null and dominant energy conditions are satisfied, while the strong energy condition is violated, which is good agreement with the recent observational studies and this reveals that the current Universe is in accelerating phase.

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

Characterizations of perfect fluid spacetimes obeying f(ℛ)-gravity equipped with different gradient solitons

The prime object of this paper is to study the perfect fluid spacetimes obeying [Formula: see text]-gravity, when [Formula: see text]-Ricci solitons, gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons are its metrics. At first, the existence of the [Formula: see text]-Ricci solitons is proved by a non-trivial example. We establish conditions for which the [Formula: see text]-Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying [Formula: see text]-gravity, when the potential vector field of [Formula: see text]-Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons in [Formula: see text]-gravity, respectively. As a result, we establish some significant theorems about dark matter era.

Static perfect fluid spacetimes on GRW spacetimes

Static perfect fluid spacetimes on GRW spacetimes

Ricci solitons on general relativistic spacetimes

The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci and gradient Ricci solitons. It is proven that if the metric of a general relativistic spacetime (M 4, ξ) admitting a special unit timelike vector field ξ is an almost Ricci soliton (g, ξ, λ), then (M 4, ξ) is a perfect fluid spacetime, and almost Ricci soliton (g, ξ, λ) on (M 4, ξ) becomes shrinking Ricci soliton. We prove that a general relativistic perfect fluid spacetime equipped with a special unit timelike vector field together with a Ricci soliton is an Einstein spacetime. In this sequel, we also prove that the Ricci soliton is shrinking, soliton vector field is Killing and the scalar curvature of the perfect fluid spacetime is constant. It is proven that a general relativistic perfect fluid spacetime together with a Ricci soliton is a generalized Robertson-Walker (GRW) spacetime. The existence of gradient Ricci solitons on general relativistic spacetimes are established. We also construct a non-trivial example of general relativistic spacetime equipped with a special unit timelike vector field, and verify some of our theorems.

CERTAIN COSMOLOGICAL MODELS WITH VARIATION OF HUBBLE PARAMETER

The present paper deals with the FRW-Cosmological Model of universe for W2 flat perfect fluid space time. Einstein field equations with variable cosmological constant (Λ) has been obtained for such spacetime and in order to get the complete cosmological solution the law of variation for Hubble’s parameter is considered. A new class of solution have been discussed for the Einstein field equations with variable cosmological constant in which the pressure, energy density, and cosmological constant Λ are found to be decreasing function of cosmic time. The physical and kinematical properties of models are also discussed.

Ricci-Yamabe Solitons in f(R)-gravity

The main objective of this paper is to describe the perfect fluid spacetimes fulfilling $f(R)$-gravity, when Ricci-Yamabe, gradient Ricci-Yamabe and $\eta$-Ricci-Yamabe solitons are its metrics. We acquire conditions for which the Ricci-Yamabe and the gradient Ricci-Yamabe solitons are expanding, steady or shrinking. Furthermore, we investigate $\eta$-Ricci-Yamabe solitons and deduce a Poisson equation and with the help of this equation, we acquire some significant results.

Relativistic spacetimes admitting almost Schouten solitons

In this paper, we investigate almost Schouten solitons and almost gradient Schouten solitons in spacetimes of general relativity. At first, it is proven that if a generalized Robertson–Walker spacetime permits an almost Schouten soliton, then it becomes a perfect fluid spacetime as well as the spacetime represents a dark matter era. Besides this, we investigate almost gradient Schouten solitons in generalized Robertson–Walker spacetimes. Moreover, a spacetime obeying almost Schouten solitons whose potential vector field is a non-homothetic conformal vector field is of Petrov type [Formula: see text] or [Formula: see text].

Solitonic Aspect of Relativistic Magneto-Fluid Spacetime with Some Specific Vector Fields

The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We exhibit that a magneto-fluid spacetime filled with a magneto-fluid density ρ, magnetic field strength H, and magnetic permeability μ obeys the Einstein field equation without the cosmic constant being a generalized quasi-Einstein spacetime manifold (GQE). In such a spacetime, we obtain an EoS with a constant scalar curvature R in terms of the magnetic field strength H and magnetic permeability μ. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci–Yamabe solitons with a time-like torse-forming vector field ξ and a φ(Ric) vector field. We establish the existence of a black hole in the relativistic magneto-fluid spacetime by demonstrating that it admits a shrinking Ricci–Yamabe soliton and satisfies the time-like energy convergence criteria. In addition, we examine the magneto-fluid spacetime with a gradient Ricci–Yamabe soliton and deduce some conditions for an equation of state (EoS) ω=−15 with a Killing vector field. Furthermore, we demonstrate that the EoS ω=−15 of the magneto-fluid spacetime under some constraints represents a star model and a static, spherically symmetric perfect fluid spacetime. Finally, we prove that a gradient Ricci–Yamabe soliton with the conditions μ=0 or H=2; μ≠0, H>2 and obeying the equation of state ω=−15 is conceded in a magneto-fluid spacetime, and a naked singularity with a Cauchy horizon subsequently emerges, respectively.

A Note on the Geometry of RW Space-Times

A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors. In each case, the form of the Ricci curvature tensor, the energy–momentum tensor, the energy density, the pressure of the fluid, and the equation of state are determined and interpreted. For example, it is demonstrated that a Ricci semi-symmetric RW space-time reduces to Einstein space-time or a Ricci recurrent RW space-time, and the perfect fluid space-time is referred to as Yang pure space-time or dark matter era.

Some physical properties of generalized quasi-Einstein spacetimes under Gray’s decomposition

In this study, we analyze generalized quasi-Einstein spacetimes endowed with Gray’s decomposition, as well as generalized Robertson–Walker spacetimes. It is shown that the Ricci tensor of a generalized quasi-Einstein spacetime assumes the form of a perfect fluid in all Gray’s subspaces under certain restrictions. Finally, it is established that a generalized quasi-Einstein generalized Robertson–Walker spacetime is a perfect fluid spacetime.

Curvature inheritance symmetry on M-projectively flat spacetimes

The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M-projective curvature tensor follows the symmetry inheritance property along a vector field [Formula: see text], when spacetime admits the conditions of both CI symmetry and conformal motion or motion along the vector field [Formula: see text]. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations (EFEs) with a cosmological term and admitting the CI symmetry along the vector field [Formula: see text]. We have shown that an M-projectively flat perfect fluid spacetime obeying the EFEs with a cosmological term and admitting the CI symmetry along a vector field [Formula: see text] is either a vacuum or satisfies the vacuum-like equation of state. We have also shown that such spacetimes with the energy–momentum tensor of an electromagnetic field distribution do not admit any curvature symmetry of general relativity. Finally, an example of M-projectively flat spacetime has been exhibited.

Characterizations of -flat curvature tensor on spacetimes and -gravity

The prime goal of this article is to characterize spacetimes endowed with -flat curvature tensor. It is demonstrated that a 4-dimensional -flat perfect fluid spacetime is either a de-Sitter spacetime or locally isometric to Minkowski spacetime under certain energy condition. Moreover, it is established that a Ricci simple -flat spacetime becomes a Robertson-Walker spacetime. In addition, we shown that a Ricci simple spacetime with harmonic -curvature tensor is a generalized Robertson-Walker spacetime. Also, we explain several conclusions based on -flat generalized Robertson-Walker spacetimes. Finally, we investigate -flat spacetimes that satisfy the -gravity and -gravity.

Horizon area bound and MOTS stability in locally rotationally symmetric solutions

In this paper, we study the stability of marginally outer trapped surfaces (MOTSs), foliating horizons of the form , embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ‘outside’ of and homologous to . Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ‘growth’ of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.

Almost co-Kähler manifolds and [formula omitted]-quasi-Einstein solitons

The present paper aims to investigate (m,ρ)-quasi-Einstein metrics on almost co-Kähler manifolds M. It is proven that if a (κ,μ)-almost co-Kähler manifold with κ<0 is (m,ρ)-quasi-Einstein manifold, then M represents a N(κ)-almost co-Kähler manifold and the manifold is locally isomorphic to a solvable non-nilpotent Lie group. Next, we study the three dimensional case and get the above mentioned result along with the manifold M3 becoming an η-Einstein manifold. We also show that there does not exist (m,ρ)-quasi-Einstein structure on a compact (κ,μ)-almost co-Kähler manifold of dimension greater than three with κ<0. Further, we prove that an almost co-Kähler manifold satisfying η-Einstein condition with constant coefficients reduces to a K-almost co-Kähler manifold, provided ma1≠(2n−1)b1 and m≠1. We also characterize perfect fluid spacetime whose Lorentzian metric is equipped with (m,ρ)-quasi Einstein solitons and acquired that the perfect fluid spacetime has vanishing vorticity, or it represents dark energy era under certain restriction on the potential function. Finally, we construct an example of an almost co-Kähler manifold with (m,ρ)-quasi-Einstein solitons.

Perfect fluid spacetimes and $k$-almost Yamabe solitons

In this article, we presumed that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and creative approach, here we study $k$-almost Yamabe solitons and gradient $k$-almost Yamabe solitons. First, two examples are constructed to ensure the existence of gradient $k$-almost Yamabe solitons. Then we show that if a perfect fluid spacetime admits a $k$-almost Yamabe soliton, then its potential vector field is Killing if and only if the divergence of the potential vector field vanishes. Besides, we prove that if a perfect fluid spacetime permits a $k$-almost Yamabe soliton ($g,k,\rho,\lambda$), then the integral curves of the vector field $\rho$ are geodesics, the spacetime becomes stationary and the isotopic pressure and energy density remain invariant under the velocity vector field $\rho$. Also, we establish that if the potential vector field is pointwise collinear with the velocity vector field and $\rho(a)=0$ where a is a scalar, then either the perfect fluid spacetime represents a phantom era, or the potential function $\Phi$ is invariant under the velocity vector field $\rho$. Finally, we prove that if a perfect fluid spacetime permits a gradient $k$-almost Yamabe soliton ($g,k,D\Phi,\lambda$) and $R, \lambda, k$ are invariant under $\rho$, then the vorticity of the fluid vanishes.

Characterizations of a spacetime admitting ψ-conformal curvature tensor

In this paper, we introduce ?-conformal curvature tensor, a new tensor that generalizes the conformal curvature tensor. At first, we deduce a few fundamental geometrical properties of ?-conformal curvature tensor and pseudo ?-conharmonically symmetric manifolds and produce some interesting outcomes. Moreover, we study ?-conformally flat perfect fluid spacetimes. As a consequence, we establish a number of significant theorems about Minkowski spacetime, GRW-spacetime, projective collineation. Moreover, we show that if a?-conformally flat spacetime admits a Ricci bi-conformal vector field, then it is either conformally flat or of Petrov type N. At last, we consider pseudo?conformally symmetric spacetime admitting harmonic ?-conformal curvature tensor and prove that the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent and also, the Ricci collineation and matter collineation are equivalent.

Some geometric and physical properties of pseudo m*-projective symmetric manifolds

In this study we introduce a new tensor in a semi-Riemannian manifold, named the M*-projective curvature tensor which generalizes the m-projective curvature tensor. We start by deducing some fundamental geometric properties of the M*-projective curvature tensor. After that, we study pseudo M*-projective symmetric manifolds (PM?S)n. A non-trivial example has been used to show the existence of such a manifold. We introduce a series of interesting conclusions. We establish, among other things, that if the scalar curvature ? is non-zero, the associated 1-form is closed for a (PM?S)n with divM* = 0. We also deal with pseudo M*-projective symmetric spacetimes, M*-projectively flat perfect fluid spacetimes, and M*-projectively flat viscous fluid spacetimes. As a result, we establish some significant theorems.