Perfect Fluid Research Articles

Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids

AbstractMotivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $$V(\phi )=\frac{(\lambda \phi )^{2n}}{2n}$$ V ( ϕ ) = ( λ ϕ ) 2 n 2 n , $$\lambda >0$$ λ > 0 , $$n\in {\mathbb {N}}$$ n ∈ N , interacting with a perfect fluid with linear equation of state $$p_{\textrm{pf}}=(\gamma _{\textrm{pf}}-1)\rho _{\textrm{pf}}$$ p pf = ( γ pf - 1 ) ρ pf , $$\gamma _{\textrm{pf}}\in (0,2)$$ γ pf ∈ ( 0 , 2 ) , in flat Robertson–Walker spacetimes. The interaction is a friction-like term of the form $$\Gamma (\phi )=\mu \phi ^{2p}$$ Γ ( ϕ ) = μ ϕ 2 p , $$\mu >0$$ μ > 0 , $$p\in {\mathbb {N}}\cup \{0\}$$ p ∈ N ∪ { 0 } . The analysis relies on the introduction of a new regular 3-dimensional dynamical systems’ formulation of the Einstein equations on a compact state space, and the use of dynamical systems’ tools such as quasi-homogeneous blow-ups and averaging methods involving a time-dependent perturbation parameter.

On the Global Well-Posedness and Analyticity of Some Electrodiffusion Models in Ideal Fluids and Porous Media

On the Global Well-Posedness and Analyticity of Some Electrodiffusion Models in Ideal Fluids and Porous Media

Physical analysis of Rastall PFRF black hole through accretion process

The adiabatic accretion onto the charged black hole surrounded by perfect fluid radiation field (PFRF) in Rastall gravity is addressed in this manuscript. For this purpose, mass accretion rate M˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{M}$$\\end{document}, critical horizon radius and some other flow parameters are being determined in the presence of polytropic fluid. Overall the process is being done analytically. The location of critical points, polytropic gas compression ratios and temperature profiles are also being investigated for different versions of polytropic equation of state. We also give the comparison of the location of critical points with case of Schwarzschild black hole in which critical points lies out side the horizon. Through above scenario, it is found that charge Q and Rastall parameter Nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{r}$$\\end{document} have deep effects on the accretion process. It is also mentioned here that under some constraints on parameters, our results reduce to Schwarzschild and charged black holes results.

Test the weak cosmic supervision conjecture in dark matter-black hole system

There is a possibility that the event horizon of a Kerr-like black hole with perfect fluid dark matter (DM) can be destroyed, providing a potential opportunity for understanding the weak cosmic censorship conjecture of black holes. In this study, we analyze the influence of the strength parameter of perfect fluid DM on the destruction of the event horizon of a Kerr-like black hole with spinning after injecting a test particle and a scalar field. We find that, when a test particle is incident on the black hole, the event horizon is destroyed by perfect fluid dark matter for extremal black holes. For nearly extremal black holes, when the dark matter parameter satisfies α∈-rh,0∪rh,k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in \\left( -r_{h} , 0\\right) \\cup \\left( r_{h} ,k_2\\right) $$\\end{document} i.e. (A<0),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(A<0),$$\\end{document} the event horizon of the black hole will not be destroyed; when the dark matter parameter satisfies α∈k1,-rh∪0,rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in \\left( k_1 ,-r_{h} \\right] \\cup \\left[ 0,r_{h}\\right] $$\\end{document} i.e. (A≥0),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(A\\ge 0),$$\\end{document} the event horizon of the black hole will be destroyed. When a classical scalar field is incident into the black hole in the extremal black hole case, we find that the range of mode patterns of the scalar field that can disrupt the black hole event horizon is different for different values of the perfect fluid dark matter strength parameter. In the nearly extremal black hole case, through our analysis, we have found when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0 $$\\end{document} and α≠±rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e \\pm \\ r_h$$\\end{document} i.e. A≠0,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\ e 0,$$\\end{document} the event horizon of the black hole can be disrupted. Our research results indicate that dark matter might be capable of breaking the black hole horizon, thus potentially violating the weak cosmic censorship conjecture.

On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

An Evans function for the linearised 2D Euler equations using Hill’s determinant

We study the point spectrum of the linearisation of Euler’s equation for the ideal fluid on the torus about a shear flow. By separation of variables the problem is reduced to the spectral theory of a complex Hill’s equation. Using Hill’s determinant an Evans function of the original Euler equation is constructed. The Evans function allows us to completely characterise the point spectrum of the linearisation, and to count the isolated eigenvalues with non-zero real part. We prove that the number of discrete eigenvalues of the linearised operator for a specific shear flow is exactly twice the number of non-zero integer lattice points inside the so-called unstable disc.

Geometry of Twisted Products and Applications on Static Perfect Fluid Spacetimes

In this paper, first we study the harmonicity of the functions and forms on the twisted products, and then we determine its sectional curvature. We explore some characteristics of static perfect fluid and static vacuum spacetimes on twisted product manifolds by proving the existence and obstructions on Ricci curvature. Finally, we study the problem of the existence static perfect fluid spacetime associated with the twisted generalized Robertson-Walker and standard static spacetime metrics.

Broadband surface wave attenuation in porous soil by elastic metasurfaces

To mitigate surface waves in ambient vibration, a novel broadband elastic metasurface is proposed by periodically burying the layered in-filled pipes below the ground surface. The present metasurface is a simple structure and can be easily implemented. In contrast to the existing studies of metasurfaces in single-phase elastic soil, the coupling of elastic metasurfaces with saturated porous soil is investigated within the framework of Biot's theory. Note that Biot's poroelasticity can capture the complexity of soils in the presence of fluids. Both dispersion and transmission analysis are comprehensively conducted. The present investigation shows that the elastic metasurfaces are suitable for a wide range of fluid-saturated porous soil, and a significant surface wave attenuation is observed within the attenuation zone of elastic metasurfaces. In addition, the burying depth is the key point of the design of elastic metasurfaces. Specifically, the surface wave attenuation zone (SWAZ) will vanish when the depth is larger than three times the periodic constant. Besides, the SWAZ will be widened by stacking the layers of elastic metasurfaces. Three layers is enough for the metasurface to attenuate more than 80 % surface wave energy. Due to the similar dynamic characteristics of elastic metasurface in the fluid-saturated porous half-space compared to dry half-space, single-phased soil can be used to simplify the analysis of saturated soil with ideal fluids. To widen the scope of application in elastic metasurfaces, the feasibility of ambient vibration mitigation by elastic metasurfaces is experimentally and numerically verified. The experimental results confirm an obvious wave attenuation within the SWAZ, and the average insertion loss (IL︸) is 9.8 dB. Last but not least, the performance of elastic metasurfaces to mitigate ground-borne vibration induced by trains is numerically studied in time domain. Elastic metasurfaces outperform traditional trenches within the main frequency range, and IL︸ is increased by 3.9–7 dB. Thanks to the excellent wave attenuation performance and subwavelength thickness, these novel elastic metasurfaces are expected to open new avenues in ambient vibration mitigation in the costal area of saturated soil.

Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field

The density of a fluid or gas, which depends on the temperature, pressure and concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that an undisturbed liquid is heterogeneous. The propagation of periodic flows in viscous, uniformly stratified fluids is considered. The analysis is based on a system of fundamental equations for the transfer of energy, momentum and matter in periodic flows. Taking into account the compatibility condition, dispersion relations are constructed for two-dimensional internal, acoustic and surface linear periodic flows with a positive definite frequency and complex wave number in a compressible viscous fluid exponentially stratified by density. The temperature conductivity and diffusion effects are neglected. The obtained regularly perturbed solutions of the dispersion equations describe the conventional weakly damped waves. The families of singular solutions, specific for every kind of periodic flow, characterize the before unknown thin ligaments that accompany each type of wave. In limited cases, the constructed regular solutions transform into well-known expressions for a viscous homogeneous and an ideal fluid. Singular solutions are degenerated in a viscous homogeneous fluid or disappear in an ideal fluid. The developing method of the fundamental equation system analysis is directed to describe the dynamics and spatial structure of periodic flows in heterogeneous fluids in linear and non-linear approximations.

Spatial Dynamics and Solitary Hydroelastic Surface Waves

This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion). The theory takes the form of a review of the Kirchgässner reduction to a finite-dimensional Hamiltonian system, highlighting the refinements in the theory over the years and presenting some novel aspects including the use of a higher-order Legendre transformation to formulate the problem as a spatial Hamiltonian system, and a Riesz basis for the phase space to complete the analogy with a dynamical system. The reduced system is to leading order given by the focussing cubic nonlinear Schrödinger equation, agreeing with the result of formal weakly nonlinear theory (which is included for completeness). We give a precise proof of the persistence of two of its homoclinic solutions as solutions to the unapproximated reduced system which correspond to symmetric hydroeleastic solitary waves.

Energy condition of wormhole and thin shell by assuming conformal symmetry in teleparallel-Rastall gravity

The static spherically symmetric wormhole solution for a non-isotropic perfect fluid energy-momentum tensor within the context of teleparallel-Rastall gravity is investigated. First, by imposing static and non-static conformal symmetry on the static spherically symmetric space-time metric, we investigated the null energy condition at the throat of traversable wormholes and showed that the null energy condition in the throat and its neighborhood is violated. Secondly, with the aim of minimize the usage of exotic matter, we found regions where the energy conditions are valid at the junction surface. We found that in the static case of conformal symmetry solution, the null energy condition (NEC), weak energy condition (WEC), and Strong energy condition (SEC) are valid for different λ 0 parameters. Moreover, we obtained that for the non-static symmetric solution of conformal symmetry, the NEC and WEC are satisfied for different sets of parameters. Finally, we have explored the stable regions by the parameter η 2 (square speed of sound) for different sets of parameters.

Topological classes of thermodynamics of black holes in perfect fluid dark matter background

In this paper we explore the topological classes of thermodynamics of a family of black holes. In particular we investigate the influence of distinct fields, including the electric field, non-linear magnetic field, along with the perfect fluid matter background that can mimic dark matter in large distances. In light of these considerations, we shall henceforth denote this fluid as perfect fluid dark matter (PFDM). Our analysis reveals that the winding and topological numbers for the Schwarzschild and Kerr black holes in PFDM background are the same as the Schwarzschild and Kerr black holes, however for the Kerr-AdS background in PFDM we obtain a different topological number compared to the Kerr black hole in PFDM. Furthermore, we explore in details the interplay of electric charge and nonlinear magnetic charge, impacting the topological classes of thermodynamics both in the absence and presence of PFDM. Interestingly, it is demonstrated that the topological numbers associated with the static Hayward black holes, both in the absence and presence of PFDM, deviate from those of the Schwarzschild black hole. This observation shows that the presence of a magnetic charge introduces an additional role and can alter the topological numbers. Finally, our study culminates with the comprehensive analysis of the topological numbers pertaining to the Hayward black hole, considering the combined effects of PFDM and rotation.

Characterizations of GRW spacetimes admitting Ricci–Yamabe solitons

In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type [Formula: see text], [Formula: see text] or [Formula: see text] and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes.

Some curvature properties of perfect fluid spacetimes

In this paper we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we investigate some curvature properties of perfect fluid spacetimes. Firstly, we provide a necessary condition for a Lorentzian manifold to be a perfect fluid spacetime. We prove that a conformally flat perfect fluid space-time is a spacetime of quasi constant sectional curvature. Also, we acquire that a conharmonically flat perfect fluid spacetime represents the radiation era. Next, we show that if a stiff matter fluid obeys Yang’s equations, then the vorticity of the fluid vanishes. Moreover, we find that if the Ricci tensor is Killing, then the perfect fluid spacetime is (i) expansion-free and shear-free, and its flow is geodesic, however, not necessarily vorticity-free, and (ii) σ and p are constant. Besides, we establish that Ricci semi-symmetric or Ricci symmetric perfect fluid spacetimes represent either dark matter era, or phantom era. Finally, we acquire that if a perfect fluid is Ricci symmetric, then either the spacetime represents a dark matter era, or a static spacetime.

Impact of m-projective curvature tensor in f (, G)-gravity and f (,  m )-gravity

This article deals with the characterization of a spacetime and modified gravity, such as -gravity and -gravity endowed with the m-projective curvature tensor. At first, we show that a m-projectively flat perfect fluid spacetime satisfying Einstein’s field equations represents a dark energy era. Also, we prove that such a spacetime obeying the strong energy condition is locally isometric to Minkowski spacetime. Moreover, it is established that a m-projectively flat perfect fluid spacetime is either a de-Sitter spacetime or a Minkowski spacetime. In addition, we show that a perfect fluid spacetime admitting harmonic m-projective curvature tensor is a Robertson-Walker spacetime. Next, we study m-projectively flat perfect fluid spacetime as a solution of -gravity and -gravity theories and explain their physical meaning. Several energy conditions in terms of Ricci scalar are investigated with the models and . 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.

Retracted: Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Retracted: Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Construction of thin-shell wormhole models in the geometric representation of [formula omitted](ℛ,[formula omitted]) gravity

The “cut and paste” approach is applied to construct static thin-shell wormhole models for f(R,T)=R+ηR2+β4R+λT, where η,β,λ are arbitrary constants and R is the Ricci scalar, as well as T, stand for the trace of the stress–energy tensor of the matter fields. We use matching conditions of the theory in geometric representation in an attempt to connect two space–times across separation hypersurface Σ. Firstly, we discuss the junction conditions for the considered specific form of f(R,T) function using distribution formalism. We assume isotropic perfect fluid and the polytropic equation of state which supports the exotic matter at the throat of the shell. We study distinct components of the Lanczos equation in the context of considered gravity model and the equation of state by employing symmetry-preserving radial perturbation. The widest possible ranges of parametric values and the influence of mass are explored to check the stability and instability of static wormhole models. This is defined via 2nd derivative of potential at throat radius and acquired constraint equation in the background of f(R,T) gravity. We examine the stable and unstable behavior of constructed wormhole solutions via theoretical and graphical approaches.

Accretion around a hairy black hole in the framework of gravitational decoupling theory

We investigate astrophysical accretion onto a static and spherically symmetric hairy black hole within the framework of gravitational decoupling. To achieve this goal, we examine the accretion procedure for several types of perfect fluids, including polytropic fluid and ultra-stiff, ultra-relativistic, radiation, and sub-relativistic isothermal fluids. Moreover, we determine the critical or sonic points for numerous fluid forms that are accreting onto the black hole by utilizing the Hamiltonian dynamical approach. Additionally, the closed form of the solutions are presented for a number of fluids, which are represented in phase diagram curves. We estimate the mass accretion rate of a static and spherically symmetric hairy black hole within the framework of gravitational decoupling. These findings are helpful in constraining the parameters of black holes while physical matter accretes onto the black holes.

Reconstruction of [formula omitted] Lagrangian for various cosmological scenarios

In this paper we explore a reconstruction scheme in the background of the f(T,T) gravity theory for different cosmological scenarios, where T is the scalar torsion and T is the trace of the energy-momentum tensor. Using the reconstruction technique f(T,T) Lagrangian is constructed for different cosmological eras such as dust, ΛCDM, perfect fluid, etc. Both minimal and non-minimal matter coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed f(T,T) functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late time accelerated expansion of the universe.