Perfect Fluid Research Articles

New classes of charged 4D EGB spacetimes with vanishing Weyl curvature

AbstractThe configuration of a perfect fluid distribution in an electric field under the influence of higher curvature geometric effects introduced through the Gauss–Bonnet invariants is studied in the 4 dimensional Glavan–Lin gravity formulation. It is found that whereas a constant spatially directed gravitational potential gives isothermal behaviour in the standard theory, this is not the case when extra curvature is present in general. A physically viable stellar model is constructed by assuming the Finch–Skea potential. The geometry and electrodynamics are well behaved being regular throughout the distribution including the centre. The model passes stability tests such as the Chandrasekar adiabatic stability criterion and causality. Additionally all energy conditions are satisfied within the star. We compare the performance of the model with its Einstein counterpart and observe that the higher curvature exerts a notable influence on all the physical properties of the star.

Study of isotropic stellar models via durgapal-lake solutions in rastall system

Abstract This manuscript is dealt with the influences of Rastall factor on the physical aspects of isotropic celestial models. In this scenario, both the ideal fluid distribution and static spherically symmetry are taken into consideration. In specifically, the Durgapal-Lake solutions are taken into consideration to analyze the different characteristics of several specific compact star models like Her X-1, Vela X-1, LMC X-4 and RXJ 1856-37. Due to its innovative combination of two methodologies, this solution is a significant advancement on Durgapal-Fuloria and Lake's previous ansatz in enormous crucial eras. Using observed estimates of radii and masses of certain specific star objects, the undefined parameters in Durgapal-Lake ansatz are derived by matching conditions. The consistency of the adopted solutions is examined through the visual interpretation of matter constituents, equation of state factor, energy conditions, mass function and stability criteria corresponding to distinct choices of Rastall factor. The radially symmetric graphs of matter variables as well as the mass function are also displayed. Moreover, We present the graphical analysis for vanishing Rastall factor. It is concluded that in the context of Rastall theory, the stars under examination exhibit stable compositions with Durgapal-Lake solution, while in the context of general relativity, they exhibit instability.

Schouten-Codazzi Gravity

Abstract We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By assuming as source the energy momentum of General Relativity, we form a second order system with its geometric sector given by the sum of the Schouten tensor and a generic second order symmetric tensor complying with the following properties: (i) it must satisfy the Codazzi differential condition and (ii) it must be concomitant with the invariant characterization based on the algebraic structure of curvature tensors for specific spacetimes or classes of spacetimes. We derive and briefly discuss the properties of SCG solutions for static spherical symmetry (vacuum and perfect fluid), FLRW models and spherical dust fluids. While we do recognize that SCG is ``work in progress'' in an incipient stage that still requires significant theoretical development, we believe that the theory provides valuable guidelines in the search for alternatives to General Relativity

Stabilizing effect of the spacetime expansion on the Euler-Poisson equations in Newtonian cosmology

Abstract The validity of the cosmic no-hair theorem for polytropic perfect fluids has been established by Brauer, Rendall, and Reula [Classical and Quantum Gravity, 11(9), 1994: 2283] within the context of Newtonian cosmology, specifically under conditions of exponential expansion. This paper extends the investigation to assess the nonlinear stability of homogeneous Newtonian cosmological models under general accelerated expansion for perfect fluids. With appropriate assumptions regarding the expansion rate and decay properties of the homogeneous solution, our results demonstrate that the Euler-Poisson system admits a globally classical solution for initial data that are small perturbations to the homogeneous solution. Additionally, we establish that the solution asymptotically approaches the homogeneous solution as time tends to infinity. The theoretical framework is then applied to various types of perfect fluids, including isothermal gases, Chaplygin gases, and polytropic gases.

The isolated effect of yield stress in viscoplastic turbulent flow

Turbulent flows of viscoplastic fluids are present in several industrial and natural applications. The effects of yield stress on this problem have always been studied as a part of a larger physical context, because real viscoplastic materials have many properties that cannot be easily isolated. Direct numerical simulations have recently emerged as a viable tool for investigating non-Newtonian fluid flow in turbulent regimes. In the present work, we solve the turbulent flow of an ideal Bingham fluid, focusing on the isolated effect of yield stress. A numerical scheme for viscoplastic flows was implemented based on the lattice Boltzmann method. An outstanding characteristic of this scheme is the possibility of representing infinite viscosity by setting the relaxation frequency to zero, enabling the representation of the Bingham constitutive equation without artifacts, and producing a more accurate representation of the yield surfaces. In the turbulent channel flow simulations, the friction Reynolds number was fixed at 180, while the Bingham number varied from 0 (Newtonian) to 0.15. It is shown that unyielded portions of material travel along with the flow near the centerline. These unyielded spots do not disappear quickly, but rather have a significant lifetime. Another interesting outcome is that the yield stress increases the turbulence anisotropy, by lowering the spanwise and normal velocity fluctuations, while the streamwise component becomes higher. Reynolds stresses and budgets of turbulent kinetic energy have been analyzed regarding the increased bulk velocities that were found by increasing the yield stress.

Strong cosmic censorship in de Sitter spacetimes with dark matter

After imposing the weak energy condition on dark matter, we find that even in the absence of charge, a spherically symmetric de Sitter black hole with perfect fluid dark matter may still possess a Cauchy horizon. This paper investigates the stability of the Cauchy horizon in such a black hole under perturbations from a massless scalar field. Through numerical calculations of the massless scalar field's quasinormal modes, we discover that in this spacetime, when the black hole approaches extremality, i.e., when the dark-matter parameter b approaches its maximum value bmax, the Strong Cosmic Censorship (SCC) conjecture may be violated. This is the first instance of classical SCC violation observed in a spherically symmetric, uncharged black hole. Additionally, we explore the region of SCC violation within the parameter space ΛM2−b/bmax. Our findings indicate that as the cosmological constant increases, the violation region initially expands and then contracts.

Singular Points of the Radiation Spectrum of Leaky Surface Magnon Polarons

Within the dissipation-free approach, for a magnetic layer separating two semi-bounded ideal fluids, it is shown that, at the point of the phonon radiation spectrum where leaky surface magnon polarons of the “dark” state are formed (of interference or symmetry-protected type) at the interface with an acoustically less dense medium, both the numerator and the denominator of the input wave impedance can independently become zero (at the very point of existence of a bound state in the continuum, they vanish simultaneously). The calculation was performed for a two-sublattice model of an antiferromagnet, which simultaneously takes into account magnetoelastic, inhomogeneous exchange, and hyperfine coupling. Conditions have been found under which the mechanisms of formation of bound states in the spectrum of phonon radiation of leaky magnon polarons involving quasi-electronic or quasi-nuclear magnons are fundamentally different: elastodynamic or elastostatic.

Analytic solutions for the Bianchi I universe coupled to several barotropic perfect fluids

Analytic solutions for the Bianchi I universe coupled to several barotropic perfect fluids

Mass and spin measurements of black hole and neutron stars X-ray binaries through axisymmetric oscillation modes of thick torus

Abstract This paper examines the oscillatory behaviour of relativistic, non-self-gravitating, charged-fluid toroidal structures within the context of the Kerr metric. The primary objective is to explore how thick accretion discs influence the mass and spin measurements of black holes and neutron stars in Low-Mass X-ray Binaries (LMXBs) through Quasi-Periodic Oscillations (QPOs) models. To achieve this, we conduct a local analysis within a general relativistic framework, determining the radial epicyclic and orbital frequencies in a perfect fluid disk. The tori are modelled using a non-Keplerian distribution of specific angular momentum, and we analyse how the oscillation properties depend on the model’s angular momentum distribution parameters. Subsequently, we connect these oscillatory frequencies to high-frequency QPOs observed in low-mass X-ray binaries, enabling us to calculate the optimal mass and spin values for each studied source.

Comment on “Solitary Wave Solutions in (2+1) Dimensions: The KdV Equation Derived from Ideal Fluid Models”, IJTP (2024) 63:105

Comment on “Solitary Wave Solutions in (2+1) Dimensions: The KdV Equation Derived from Ideal Fluid Models”, IJTP (2024) 63:105

Development of the wave motion induced by near-bottom periodic disturbances in a two-layer shear current

The behavior of wave motion arising in an ideal incompressible homogeneous fluid under switching-on periodic bottom disturbances is studied in the linear approximation for the two-dimensional non-stationary problem. In the undisturbed state, the velocities of two-layer fluid flow are linear functions of the vertical coordinate in each of the layers with different gradients and coincide on the boundary of the layers. The upper boundary of fluid can be either free or bounded by the rigid cover. The dispersion dependences and the group velocities of the appearing wave modes are determined. The vertical displacements of the free surface and the interface between the layers are calculated. A comparison with the solution for a single-layer fluid is carried out.

Cosmological implications on two fluids model universe with parametrization of Hubble parameter in Lyra manifold

In this research, we explore the cosmological implication on five-dimensional FRW cosmological model for k = 0 in presence of two perfect fluids: ordinary baryonic fluid and an interacting dark energy in the context of Lyra’s manifold. We obtain an exact solution of the field equations by assuming the parametrization of the Hubble parameter H(a) = τ(1 + a −ν ), where a is a scale factor and τ > 0, ν > 1 are the arbitrary constants. This results in a universe model with a transition from a previously decelerating universe to the current accelerating universe, characterized by a time-dependent deceleration parameter. Moreover, we have used 46 observational Hubble data sets to restrict the parameters of our suggested model. Some cosmological parameters have been examined about the nature of the proposed model universe. It is shown that our model can be considered a realistic one.

Non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter: Plasma lensing and thermodynamics analysis

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.

Modified F(R,T2)-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

In the present research note, we discuss the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the F(R,T2)-gravity model. Furthermore, we deal with the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to F(R,T2)-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential Un with hyperbolic Ricci solitons in the F(R,T2)-gravity model coupled with perfect fluid and a phantom barrier.

Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field Bi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{i}$$\\end{document} is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field Ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{i}$$\\end{document} is irrotational. We identify the conditions to ensure both Bi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{i}$$\\end{document} and Ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{i}$$\\end{document} of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by p=4-n2n-2μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\frac{4-n}{ 2n-2}\\mu $$\\end{document}, whereas in a pseudo Ricci symmetric space-time, the state equation takes the form p=3-nn-1μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\frac{3-n}{n-1}\\mu $$\\end{document}, where p and μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} are the isotropic pressure and the energy density. It is noteworthy that if n=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=4$$\\end{document} , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era.

Generalized Brenier Principle and the Closure Problem of Landgren–Monin–Novikov Hierarchy for Vorticity Field

Brenier’s concept – a representation of solutions to the equations of ideal incompressible fluids in terms of probability measures on the set of Lagrangian trajectories in the case of their stochasticity, is a generalization of Arnold’s principle of least action of finding smooth solutions of Euler’s equations. In this work, the variational generalized Brenier principle (Brenier, J. Am. Math. Soc. 1989) is used to close the infinite chain of Landgren–Monin–Novikov equations for the n-point probability density functions fn of the vortex field of two-dimensional turbulence. In addition, within the framework of the statistical approach, an approximation of the variational problem with conditions at the ends posed by Shnirelman (Mat. Sat. 1985) for the Euler equation is proposed.

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

Enigmatic factor of 4/3 in electromagnetic momentum of a moving spherical capacitor

The electromagnetic energy–momentum of a moving charged spherical capacitor may be calculated by a 4-vector Lorentz transformation from the energy in the rest frame. However, energy–momentum of the moving system computed directly from electromagnetic fields yields extra terms; in particular a factor of 4/3 in momentum appears, similar to that encountered in the classical electron model, where this enigmatic factor has been a source of confusion for more than a century. There have been many attempts to eliminate this ‘unwanted’ factor, noteworthy among them is a modification in electromagnetic field energy–momentum definition that has entered even standard textbooks. Here it is shown that in a moving charged spherical capacitor, such a factor of 4/3 in the electromagnetic momentum arises naturally from electromagnetic forces in system or equivalently from terms in the Maxwell stress tensor; contributions that do not otherwise show up in 4-vector transformations. A similar factor of 4/3 in the momentum of a perfect fluid comprising a randomly moving ultra-relativistic gas molecules or an isotropic photon gas, filling an uncharged spherical capacitor in motion, appears owing to the contribution of pressure. Thus, genesis of the ‘enigmatic’ factor of 4/3 can be traced to pressure or stress whose presence in the system may even be of non-electromagnetic origin and where the proposed modifications in energy–momentum definition do not even come into picture, implying there is no justification in modifying the standard definition of electromagnetic energy–momentum.

A dissipative extension to ideal hydrodynamics

Abstract We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established Müller-Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit.

Investigation on hyperbolic Ricci soliton in a perfect fluid spacetime

The aim of this paper is to inspect the geometrical aspects of a perfect fluid spacetime conveying hyperbolic Ricci soliton with torse-forming vector field [Formula: see text]. Next, we have investigated some physical perceptions of perfect fluid spacetime such as dark fluid spacetime, stiff matter fluid spacetime, dust fluid spacetime and radiation fluid spacetime with hyperbolic Ricci soliton in terms of isotropic pressure, the cosmological constant, energy density and gravitational constant. We have also provided two examples of hyperbolic Ricci soliton and hyperbolic Ricci–Bourguignon soliton. Later, we explore the relativistic magneto-fluid spacetime obeying hyperbolic Ricci soliton along with different vector fields.