Perfect Fluid Case Research Articles

Late time cosmological solutions in f(R,T) gravity in a viscous universe

Considering the condition on conservation of energy–momentum tensor (EMT), we study late time cosmological solutions in the context of [Formula: see text] gravity (where [Formula: see text] and n are constants) in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. The present model discusses the case of a barotropic perfect fluid as the matter content of the Universe, along with the case when dissipative effects are taken into account. Briefly, assuming a single perfect fluid, we find that the mentioned model is not capable of presenting an observationally consistent picture of the late time accelerated expansion of the Universe; nevertheless, the model leads to admissible solutions when the bulk viscosity is included. In this regard, a consistent setting is found considering the Eckart, Truncated and Full Israel–Stewart theories which determine the behavior of bulk viscosity. In the presence of bulk viscosity, the behavior of the deceleration parameter (DP) shows that the underlying model can describe an acceptable evolution even if the isotropic pressure of matter content of the Universe is negligible.

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.

Novel features of attractors and transseries in nonconformal Bjorken flows

In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the nonconformal hydrodynamic equations of a longitudinal boost invariant expanding plasma. The new transseries solutions unveil a rich physical structure which arises due to the interplay of different physical scales. In the perfect fluid case the nonconformal speed of sound slows down the cooling of the temperature due to the emergence of logarithmic corrections that depends on the mass of the particle. These terms propagate into the perturbative and nonperturbative sectors of the transseries once viscous corrections are included. The logarithmic mass contributions increase the asymptotic value of the Knudsen number while decreasing the damping rate of the transient nonhydrodynamic modes and thus, yielding to an extremely slow hydrodynamization process where flow lines merge to their forward attractor at extremely late times. The early time free streaming expansion is modified and receives logarithmic mass corrections induced by the shear-bulk couplings. The global flow structure and numerical analyses carried out in our work demonstrate the existence of local attraction at early and late times for the shear viscous tensor and bulk viscous pressure.

A Probe into a (2 + 1)-Dimensional Combined Cosmological Model in f(R, T) Gravity

This research is an extension of our earlier published (2+1) dimensional cosmological models in f(R,T) gravity with Λ(R,T) (IOP Conf. Ser. J. Phys. Conf. Ser. 2019, 1258, 012026). A different class of cosmological space model is studied under modified theories of f(R,T) gravity, where the cosmological constant Λ is expressed as a function of the Ricci scalar R and the trace of the stress-energy momentum tensor T. We call such a model as “Λ(R,T) gravity”. Such a specific form of Λ(R,T) has been defined in the dust as well as in the perfect fluid case. We intend to search for a combined model that satisfies the equation of state for dark energy matter or quintessence matter or perfect matter fluid. Some geometric and intrinsic physical properties of the model are also described. The energy conditions, pressure and density are discussed both when Λ=Λ(r) is a function of the radial parameter r, as well as when Λ is zero. We study the effective mass function and also the gravitational redshift function, both of which are found to be positive as per the latest observations. The cosmological model is studied in f(R,T) modified theory of gravity, where the gravitational Lagrangian is expressed both in terms of the Ricci scalar R and the trace of the stress-energy tensor T. The equation of state parameter is discussed in terms of ω corresponding to the three cases mentioned above. The behaviour of the cosmological constant is separately examined in the presence of quintessence matter, dark energy matter and perfect fluid matter.

Effect of inertia on the dynamic contact angle in oscillating menisci

The contact angle between a gas–liquid interface and a solid surface is a function of the dynamic conditions of the contact line. Classic steady correlations link the contact angle to the contact line velocity. However, it is unclear whether they hold in the presence of inertia and the case of perfect wetting fluids. We analyze by means of experiments the shape of a liquid interface and the corresponding contact angle in accelerating conditions for two different fluids, that is, HFE7200 (perfect wetting) and demineralized water. The setup consists of a U-shaped quasi-capillary tube in which the liquid column oscillates in response to a pressure step on one of the two sides. We obtained the evolution of the interface shape from high-speed back-light visualization, fit interface models to the experimental data to estimate the contributions of all the governing forces, and perform measurements of the dynamic contact angle. We propose a new model to account for the impact of the interface acceleration on its shape, and we discuss the impact on the measurement of the transient contact angle. The new model allows us to perform dynamic contact angle measurements below 15°, which is challenging to obtain with traditional techniques. We show for the first time a dynamic characterization of the wetting behavior of HFE7200, and we compare the results with traditional hydrodynamic models.

Compact elastic objects in general relativity

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)\approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfect fluid case, and then obtain the thermodynamical criterion for radial perturbation. We show that these two stability criterion are the same, which suggest that the inherent connection between gravity and thermodynamic even when the electric field is taken into account.

A simple geometry to model fluid spheres in general relativity

A simple geometry which is static and spherically symmetrical is proposed, useful to model a fluid sphere in general relativity. This allows us to describe the interior of stellar objects both neutral and charged. It is shown that in both cases the solution is stable, which means that the behavior of the density and radial pressure is monotonic decreasing functions. Both models depend on two parameters, in the neutral case, these are the compactness rate $$u=GM/c^2R$$ and w related to the monotonically increasing or decreasing behavior of the speed of sound, and in the charged case, they are the compactness rate and the rate between the charge Q and the radius R, $$q=Q/R$$ . A comparison is done between the case of a charged perfect fluid and the case of an anisotropic fluid; from there we can show that, as a result of the presence of the charge and its repulsion effect that it generates at a local and universal level, the density for the anisotropic case is greater than the density in the charged case. For both models, we obtain physical values of objects with a compactness rate $$u=0.35578$$ for the particular cases of masses and radios for $$(M_\odot ,R=4150.1\,\mathrm{m})$$ , $$(1.5M_\odot ,R=6225\,\mathrm{m})$$ , $$(2M_\odot ,R=8300 m)$$ . In the neutral case, the greater central density $$\rho _c=5.0840\times 10^{19} \,\mathrm{kg/m}^3$$ matches the object of $$1.5M_\odot $$ and for the charged case, the maximum central density is of $$\rho _c=8.8439\times 10^{18} \,\mathrm{kg/m}^3$$ , associated with the star with $$1M_\odot $$ . Additionally, by using the proposed model, we obtain the values of density and pressure for the star PSR J1614–223, the maximum value of the central density $$\rho _c=1.0573\times 10^{18} \,\mathrm{kg/m}^3$$ .

Effects of nonlinearity of f(R) gravity and perfect fluid in Kaluza\u2013Klein models with spherical compactification

We study the effects associated with nonlinearity of f(R) gravity and of the background perfect fluid manifested in the Kaluza–Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with f^{prime prime }(R_0)ne 0, we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some “corrupted” prefactor (in front of the exponential function), which, in addition to the standard 1/r term, contains a contribution independent of the three-dimensional distance r. In the linear f''(R)=0 model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of f''(R_0)=0.

Stability analysis and constraints on interacting viscous cosmology

In this work we study the evolution of a spatially flat Universe by considering a viscous dark matter and perfect fluids for dark energy and radiation, including an interaction term between dark matter and dark energy. In the first part, we analyse the general properties of the Universe by performing a stability analysis and then we constrain the free parameters of the model using the latest and cosmological-independent measurements of the Hubble parameter. We find consistency between the viscosity coefficient and the condition imposed by the second law of the Thermodynamics. The second part is dedicated to constrain the free parameter of the interacting viscous model (IVM) for three particular cases: the viscous model (VM), interacting model (IM), and the perfect fluid case (the concordance model). We report the deceleration parameter to be $q_0 = -0.54^{+0.06}_{-0.05}$, $-0.58^{+0.05}_{-0.04}$, $-0.58^{+0.05}_{-0.05}$, $-0.63^{+0.02}_{-0.02}$, together with the jerk parameter as $j_0 = 0.87^{+0.06}_{-0.09}$, $0.94^{+0.04}_{-0.06}$, $0.91^{+0.06}_{-0.10}$, $1.0$ for the IVM, VM, IM, and LCDM respectively, where the uncertainties correspond at 68\% CL. Worth mentioning that all the particular cases are in good agreement with LCDM, in some cases producing even better fits, with the advantage of eliminating some problems that afflicts the standard cosmological model.

(2+1) dimensional cosmological models in f(R, T) gravity with (R, T)

We intend to study a new class of cosmological models in f(R, T) modified theories of gravity, hence define the cosmological constant as a function of the trace of the stress energy-momentum-tensor T and the Ricci scalar R, and name such a model Λ(R, T) gravity where we have specified a certain form of Λ(R, T). Λ(R, T) is also defined in the perfect fluid and dust case. Some physical and geometric properties of the model are also discussed. The pressure, density and energy conditions are studied both when Λ is a positive constant and when Λ = Λ(t), i.e a function of cosmological time, t. We study behavior of some cosmological quantities such as Hubble and deceleration parameters. The model is innovative in the sense that it has been described in terms of both R and T and display better understanding of the cosmological observations.

Multi-gradient fluids

An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton’s principle, we obtain a thermodynamical form of the equation of motion which generalizes the case of perfect compressible fluids. First integrals of flows are extended cases of perfect compressible fluids. The equation of motion and the equation of energy are written for dissipative cases, and are compatible with the second law of thermodynamics.

Brane world models with bulk perfect fluid and broken 4D Poincaré invariance

We consider 5D brane world models with broken global 4D Poincar\a'{e} invariance (4D part of the spacetime metric is not conformal to the Minkowski spacetime). The bulk is filled with the negative cosmological constant and may contain a perfect fluid. In the case of empty bulk (the perfect fluid is absent), it is shown that one brane solution always has either a physical or a coordinate singularity in the bulk. We cut off these singularities in the case of compact two brane model and obtain regular exact solutions for both 4D Poincar\a'{e} broken and restored invariance. When the perfect fluid is present in the bulk, we get the master equation for the metric coefficients in the case of arbitrary bulk perfect fluid equation of state (EoS) parameters. In two particular cases of EoS, we obtain the analytic solutions for thin and thick branes. First one generalizes the well known Randall-Sundrum model with one brane to the case of the bulk anisotropic perfect fluid. In the second solution, the 4D Poincar\a'{e} invariance is restored. Here, the spacetime goes asymptotically to the anti-de Sitter one far from the thick brane.

Cosmological nonlinear structure formation in full general relativity

We perform numerical evolutions of cosmological scenarios using a standard general relativistic code in spherical symmetry. We concentrate on two different situations: initial matter distributions that are homogeneous and isotropic, and perturbations to those that respect the spherical symmetry. As matter models we consider the case of a pressureless perfect fluid, i.e. dust, and the case of a real massive scalar field oscillating around the minimum of the potential. Both types of matter have been considered as possible dark matter candidates in the cosmology literature, dust being closely related to the standard cold dark matter paradigm. We confirm that in the linear regime the perturbations associated with these types of matter grow in essentially the same way, the main difference being that in the case of a scalar field the dynamics introduce a cut-off in the power spectrum of the density perturbations at scales comparable with the Compton wavelength of the field. We also follow the evolutions well beyond the linear regime showing that both models are able to form structure. In particular we find that, once in the nonlinear regime, perturbations collapse faster in a universe dominated by dust. This is expected to delay the formation of the first structures in the scalar field dark matter scenario with respect to the standard cold dark matter one.

An alternative f(R, T) gravity theory and the dark energy problem

Recently, a generalized gravity theory was proposed by Harko et al. where the Lagrangian density is an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, known as F(R,T) gravity. In their derivation of the field equations, they have not considered conservation of the stress-energy tensor. In the present work, we have shown that a part of the arbitrary function f(R,T) can be determined if we take into account of the conservation of stress-energy tensor, although the form of the field equations remain similar. For homogeneous and isotropic model of the universe the field equations are solved and corresponding cosmological aspects has been discussed. Finally, we have studied the energy conditions in this modified gravity theory both generally and a particular case of perfect fluid with constant equation of state.

Killing and Noether Symmetries of Plane Symmetric Spacetime

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkwoski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries [1].

High-Speed Cylindrical Collapse of Type-I Matter

In this paper, the cylindrical symmetric grav- itational collapse with anisotropic pressure has been investigated using high-speed approximation scheme. The collapsing speed of the fluid is assumed to be very large. To see the effects of pressure, we have used the equations √ pR/ρ = k and √ pT /ρ = w of states for radial pressure and tangential pres- sure, respectively. It is observed that if the ra- tios of both pressures, that is, tangential and radial pressures, to energy density are bounded from be- low by some positive value, there arise two pos- sibilities depending on whether 1 + k 2 − 2w 2 > 0 or 1 + k 2 − 2w 2 0, the high-speed approximation scheme fails, while for 1+k 2 −2w 2 < 0, the high-speed approximation works. For vanishing w and k, the high-speed scheme does not break down, and, as a result, a naked singularity forms in this case. For pT = pR = p, all the results reduce to the perfect fluid case obtained by Nakao and Morisawa (Prog Theor Phys 113:73, 2005).

Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter

This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter. It is shown that solutions whose matter source is sufficiently close to being isotropic exhibit the same qualitative dynamics as perfect fluid solutions. However a high degree of anisotropy of the matter model can cause dynamics to differ significantly from the vacuum and perfect fluid case.

A rotating three component perfect fluid source and its junction with empty space-time

The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein's equations. It is shown that these solutions are the familiar static perfect fluid cases commonly derived in curvature coordinates but now endowed with rotation. The resulting solutions are also discussed in the context of T-solutions of Einstein's equations and the vacuum T-solution outside a rotating source is presented. The interior source for these solutions is shown not to be a perfect fluid but rather an anisotropic three component perfect fluid for which the energy momentum tensor is derived. The Schwarzschild interior solution is given as an example of the approach.

Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry

By studying the Gödel-type solution, the causality in f(R) gravity with an arbitrary coupling between matter and geometry is discussed. Assuming that the matter source is a perfect fluid and a scalar field, respectively, we find that for the perfect fluid case, noncausal Gödel-type solutions exist and there is a critical radius rc beyond which the causality is violated. For the scalar field case, the violation of causality is forbidden.