Perfect Fluid Models Research Articles

Generalized quasi-conformal curvature tensor and the spacetime of general relativity

In this paper, a study of generalized quasi-conformal curvature tensor has been made on the four dimensional spacetime of general relativity. Some results related to the application of such spacetime in the general relativity are obtained. Perfect fluid and dust fluid cosmological models have also been studied.

Fluid modeling of CF3I/CO2 arc formation process

The environmentally friendly insulating gas CF3I is a promising replacement for SF6 due to its excellent insulation and arc extinguishing performance. In the arc chamber of high-voltage circuit breakers filled with CF3I/CO2, the near-electrode sheath dominates the current transfer process between contact and arc column during arc formation, which has a significant effect on the transition from glow to arc discharge. The 30%CF3I/70%CO2 was taken as the research object in this research, and a more perfect fluid model was established considering the influence of diffusion current. The arc formation process between the contacts at the preliminary stage of circuit breaker interruption was conducted. The results show that the arc formation process can be divided into three stages: glow discharge, abnormal glow discharge, and arc discharge. As the arc formation process proceeds, the thickness of the near-cathode sheath decreases gradually. When the arc reaches stability with the current density 8×106–1.6×107A·m−2, the thickness of the near-cathode sheath is 7 μm, the steep voltage fall near the cathode sheath is generated within 7 μm away from the cathode surface, and this voltage fall almost does not change with the current density. CF3I− is the dominant negative ion between the contacts, which indicates that CF3I has excellent electron adsorption performance and is beneficial to arc deionization. The computational results of this work were compared with the existing experimental ones, which shows that the model used in this work is accurate enough. Finally, suggestions for model optimization and future work are given.

Hamiltonian Formalism for Bianchi Type I Model for Perfect Fluid as Well as for the Fluid with Bulk and Shearing Viscosity

Hamiltonian Formalism for Bianchi Type I Model for Perfect Fluid as Well as for the Fluid with Bulk and Shearing Viscosity

Energy conditions in extended f(R, G, T) gravity

In this paper, we consider the flat FriedmannLematreRobertson-Walker metric in the presence of perfect fluid models and extended f(R, G, T) gravity (where R is the Ricci scalar, G is the Gauss Bonnet invariant and T stands for trace of energy momentum tensor). In this context, we assume some specific realistic f(R, G, T) models configuration that could be used to explore the finite-time future singularities that arise in late-time cosmic accelerating phases. In this scenario, we choose the most recent estimated values for the Hubble, deceleration, snap and jerk parameters to develop the viability and bounds on the models parameters induced by different energy conditions.

Viscous cosmology in f(T) gravity

We propose a new model for the viscosity of cosmic matters, which can be applied to different epochs of the universe. Using this model, we include the bulk viscosities as practical corrections to the perfect fluid models of the baryonic and dark matters since the material fluids in the real world may have viscosities due to thermodynamics. Such inclusion is put to the test within the framework of f(T) gravity that is proved to be successful in describing the cosmic acceleration, where T denotes the torsion scalar. We perform an observational fit to our model and constrain the cosmological and model parameters by using various latest cosmological datasets. Based on the fitting result, we discuss several cosmological implications including the dissipation of matters, the evolutionary history of the universe, f(T) modification as an effective dark energy, and the Hubble tension problem. The corresponding findings are (i) The late time dissipation will make the density parameters of the matters vanish in the finite future. Moreover, the density ratio between the baryonic and dark matters will change over time. (ii) The radiation dominating era, matter dominating era and the accelerating era can be recovered and the model can successfully describe the known history of the universe. (iii) The f(T) modification is the main drive of the acceleration expansion and currently mimics a phantom-like dark energy. But the universe will eventually enter a de Sitter expansion phase. (iv) The Hubble tension between local and global observations can be significantly alleviated in our model.

Quantum cosmological perfect fluid models in Einstein aether theory

Quantum cosmological perfect fluid models in Einstein aether theory

An isotropic compact stellar model in curvature coordinate system consistent with observational data

This paper investigates a spherically symmetric compact relativistic body with isotropic pressure profiles within the framework of general relativity. In order to solve the Einstein’s field equations, we have considered the Vaidya–Tikekar type metric potential, which depends upon parameter K. We have presented a charged perfect fluid model, considering $$K\notin [0,1]$$ , which represent compact stars like Her X-1, 4U 1538-52, SAX J1808.4-3658, LMC X-4, SMC X-4, EXO 1785-248, Cen X-3 and Cyg X-2, to an excellent degree of accuracy. We have investigated the physical features such as the energy conditions, velocity of sound, surface redshift, adiabatic index of the model in detail and shown that our model obeys all the physical requirements for a realistic stellar model. Using the Tolman–Oppenheimer–Volkoff equations, we have explored the hydrostatic equilibrium and the stability of the compact objects. This model also fulfils the Harrison–Zeldovich–Novikov stability criterion. We have checked the behaviour of the system in the presence of a very high charge (around $$10^{20}$$ Coulomb at surface), which causes an electric field intensity above the Schwinger limit. This amount of charge is mainly caused due to very high density of the system, and a dense system like a compact star can contain such a huge charge. The results obtained in this paper can also be used in analysing other isotropic compact objects.

Probing elastic interactions in the dark sector and the role of S8

We place observational constraints on two models within a class of scenarios featuring an elastic interaction between dark energy and dark matter that only produces momentum exchange up to first order in cosmological perturbations. The first one corresponds to a perfect-fluid model of the dark components with an explicit interacting Lagrangian, where dark energy acts as a dark radiation at early times and behaves as a cosmological constant at late times. The second one is a dynamical dark energy model with a dark radiation component, where the momentum exchange covariantly modifies the conservation equations in the dark sector. Using Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and Supernovae type Ia (SnIa) data, we show that the Hubble tension can be alleviated due to the additional radiation, while the $\sigma_8$ tension present in the $\Lambda$-Cold-Dark-Matter model can be eased by the weaker galaxy clustering that occurs in these interacting models. Furthermore, we show that, while CMB+BAO+SnIa data put only upper bounds on the coupling strength, adding low-redshift data in the form of a constraint on the parameter $S_8$ strongly favours nonvanishing values of the interaction parameters. Our findings are in line with other results in the literature that could signal a universal trend of the momentum exchange among the dark sector.

Perfect fluid model with g = 2

A perfect fluid model with a shell of charge is presented which yields g = 2 for low angular velocity. This model is not intended to represent a classical model of the electron but to show that a simple model based on equations consistent with special relativity can yield a value of g = 2.

Reheating after an Inflationary Universe from a Perfect Fluid and Its Comparison with Observational Data

Abstract We present the reheating constraints on an inflationary universe induced by perfect fluid models. Starting with the descriptions for the observables of the scalar field inflationary models in the reconstructed methods, we outline the procedure of perfect fluid inflationary models through these methods to calculate the inflationary observables and reheating. We show that the reheating e-folds number N re and the reheating final temperature T re are bound depending on the finite range of reasonable values of . By restricting the equation-of-state parameter in the reheating stage, , more stringent constraints can be derived for the model’s parameter space of perfect fluid. These constraints correspond to viable values of the scalar spectral index n s and tensor-to-scalar ratio r, released by Planck2018 observational data.

Cosmic censorship of trans-Planckian field ranges in gravitational collapse

A classical solution where the (scalar) field value moves by an O(1) range in Planck units is believed to signal the breakdown of Effective Field Theory (EFT). One heuristic argument for this is that such a field will have enough energy to be inside its own Schwarzschild radius, and will result in collapse. In this paper, we consider an inverse problem: what kind of field ranges arise during the gravitational collapse of a classical field? Despite the fact that collapse has been studied for almost a hundred years, most of the discussion is phrased in terms of fluid stress tensors, and not fields. An exception is the scalar collapse made famous by Choptuik. We re-consider Choptuik-like systems, but with the emphasis now on the evolution of the scalar. We give strong evidence that generic spherically symmetric collapse of a massless scalar field leads to super-Planckian field movement. But we also note that in every such supercritical collapse scenario, the large field range is hidden behind an apparent horizon. We also discuss how the familiar perfect fluid models for collapse like Oppenheimer-Snyder and Vaidya should be viewed in light of our results.

Analytic radiation model for perfect fluid under homotopy perturbation method

An expression for mass of a spherically symmetric system is obtained by solving the Tolman–Oppenheimer–Volkoff equation, employing the homotopy perturbation method. With the help of this expression and the Einstein field equations, a set of interior solutions is arrived at. Thereafter, different aspects of the solution are explained as regards mass, density, pressure, energy, stability, mass–radius ratio, compactness factor and surface redshift. This analysis shows that all the physical properties, in connection to brown dwarf stars, are valid with the observed features.

Concircular vector fields and the Ricci solitons for the LRS Bianchi type-V spacetimes

The purpose of this paper is to explore concircular vector fields (CVFs) of locally rotationally symmetric (LRS) Bianchi type-V spacetimes and to investigate whether these CVFs are Ricci soliton vector fields. We first obtained the concircular equations and then solved them by integrating directly. The existence of concircular symmetry imposes restrictions on the metric functions. It is shown that Bianchi type-V spacetimes admit four-, five-, six-, seven-, eight- or fifteen-dimensional CVFs. Further, we studied the Ricci soliton vector fields for all the cases where Bianchi type-V spacetimes admit CVFs. For this purpose, the obtained CVFs are substituted into Ricci soliton equations. These equations imposed further restrictions on metric functions and it is shown in each case that either all or some CVFs are also Ricci soliton vector fields. The gradient of Ricci soliton vector fields are also obtained. It is shown that the metrics that admit CVFs represent physically plausible perfect fluid models under certain conditions.

Static spherically symmetric Einstein-æther models II: Integrability and the modified Tolman–Oppenheimer–Volkoff approach

We investigate the existence of analytic solutions for the field equations in the Einstein-æther theory for a static spherically symmetric spacetime and provide a detailed dynamical systems analysis of the field equations. In particular, we investigate if the gravitational field equations in the Einstein-æther model in the static spherically symmetric spacetime possesses the Painlevè property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansions only when the matter source consists of a perfect fluid with a linear equation of state (EoS) μ=μ0+h−1p,h>1. In order to study the field equations we apply the Tolman–Oppenheimer–Volkoff (TOV) approach and other approaches. We find that the relativistic TOV equations are drastically modified in Einstein-æther theory, and we explore the physical implications of this modification. We study perfect fluid models with a scalar field with an exponential potential. We discuss all of the equilibrium points and discuss their physical properties.

A perfect fluid model for compact stars

In the framework of Einstein's the theory of general relativity we present a new interior solution with a perfect fluid, this is constructed from the proposal of a gravitational redshift factor. The geometry is regular and its density and pressure are monotonic decrescent functions, furthermore the sound speed is smaller than the light speed and monotonic crescent. The solution depends on a parameter $w \in (0, 2.0375509325]$ related to the compactness of the star $u = GM/c^2 R$, the maximum value $u = 0.2660858316$ which allow to describe compact stars like quark stars or neutron stars. Although there is a diversity of stars for which the model can be used, we only apply this solution to describe the interior of a neutron star PSR J0348$+$0432. According to the observations, it is known that its mass $M = (2.01 \pm 0.04)M_{\odot}$ and its radius is between 12.062Km and 12.957Km, so the value of the compactness is in the range $u \in [0.2244845, 0.2509338]$. In addition to the decreasing behavior of the mentioned pressure and density functions, the results are consistent with the density values range typical of neutron stars and the maximal central density of the star result to be 1.283818 $\times 10^{18} Kg/m^{3}$.

A charged perfect fluid model with high compactness

A relativistic, static and spherically symmetrical stellar model is presented, constituted by a perfect charged fluid. This represents a generalization to the case of a perfect neutral fluid, whose construction is made through the solution to the Einstein-Maxwell equations proposing a form of gravitational potential $g_{tt}$ and the electric field. The choice of electric field implies that this model supports values of compactness$u=GM/c^2R\leq 0.5337972212$, values higher than the case without electric charge ($u\leq 0.3581350065$), being this feature of relevance to get to represent compact stars. In addition, density and pressure are positive functions, bounded and decreasing monotones, the electric field is a monotonously increasing function as well as satisfying the condition of causality so the model is physically acceptable. In a complementary way, the internal behavior of the hydrostatic functions and their values are obtained taking as a data the corresponding to a star of $1 M_\odot$,for different values of the charge parameter, obtaining an interval for the central density $\rho_c\approx (7.9545,2.7279) 10^{19}$ $ Kg/m^3$ characteristic of compact stars.

A regular perfect fluid model for dense stars

We present an exact regular solution of Einstein equations for a static and spherically symmetric spacetime with a matter distribution of isotropic perfect fluid. The construction of the solution is realized assigning a regular potential [Formula: see text] and integrating the isotropic perfect fluid condition for the pressure. The resulting solution is physically acceptable, i.e. the geometry is regular and the hydrostatic variable pressure and density are positive regular monotonic decreasing functions, the speed of the sound is positive and smaller than the speed of the light. An important element of this solution is that its compactness value [Formula: see text] is in the characteristic range of compact stars, which makes a remarkable difference with other models with isotropic perfect fluid, this is [Formula: see text] so that we could represent compact stellar objects as neutron stars. In particular, for the maximum compactness of a star with a mass of [Formula: see text] the radius is [Formula: see text] and their central density [Formula: see text] is characteristic of compact stars.

Delta Shock Wave in a Perfect Fluid Model with Zero Pressure

Abstract The Riemann problem for a perfect fluid model with zero pressure is considered, where the external force is a given continuous function of time. All of exact solutions are given. In particular, a vacuum occurs in the solutions, although initial data stay far away from the vacuum. It is shown that a delta shock wave in which density and internal energy contain a Dirac delta function develops in the solutions. The position, velocity, and weights of the delta shock wave are presented explicitly. Moreover, all of the solutions are not self-similar because of the presence of the external force.

A perfect fluid model for neutron stars

In this paper, we present a physically acceptable internal solution with a perfect fluid, which needs the pressure and density as regular, positive and monotonic decreasing functions and with a speed of sound positive and lower than the speed of light. This solution depends on a parameter [Formula: see text], and it is physically acceptable if [Formula: see text], the compactness has a maximum value for the maximum value of [Formula: see text] and it corresponds to [Formula: see text], thus the model can be applicable to the description of compact stars. In a complementary way, we present the description of a star with mass equal to the sun mass and radius of [Formula: see text] Km associated to the neutron star Her X-1, obtaining a central density [Formula: see text] which is characteristic of the neutron stars.

Long-term evolution of CFS-unstable neutron stars and the role of differential rotation on short time-scales

Abstract I consider differential rotation, associated with radiation-driven Chandrasekhar–Friedman–Schutz (CFS) instability, and respective observational manifestations. I focus on the evolution of the apparent spin frequency, which is typically associated with the motion of a specific point on the stellar surface (e.g. polar cap). I start from long-term evolution (on the time-scale when instability significantly changes the spin frequency). For this case, I reduce the evolution equations to one differential equation and I demonstrate that it can be directly derived from energy conservation law. This equation governs the evolution rate through a sequence of thermally equilibrium states and it provides linear coupling for the cooling power and rotation energy losses via gravitational wave emission. In particular, it shows that differential rotation does not affect long-term spin-down. In contrast, on short time-scales, differential rotation can significantly modify the apparent spin-down, if we examine a strongly unstable star with a very small initial amplitude for the unstable mode. This statement is confirmed by considering a Newtonian non-magnetized perfect fluid and dissipative stellar models as well as a magnetized stellar model. For example, despite the fact that the widely applied evolution equations predict effective spin to be constant in the absence of dissipation, the CFS-unstable star should be observed as spinning-down. However, the effects of differential rotation on apparent spin-down are negligible for realistic models of neutron star recycling, unless the neutron star is non-magnetized, the r-mode amplitude is modulated faster than the shear viscosity dissipation time-scale, and the amplitude is large enough that spin-down can be measured on a modulation time-scale.