Self-gravitating Fluid Research Articles

Charged anisotropic spherical collapse in f(R,T,Q) gravity

This paper discusses the gravitational collapse of dynamical self-gravitating fluid distribution in f ( R , T , Q ) gravity, where Q = R φ ϑ T φ ϑ . In this regard, we assume a charged anisotropic spherical geometry involving dissipation flux and adopt standard model of the form R + Φ T + Ψ Q , where Φ and Ψ symbolize real-valued coupling parameters. The Misner–Sharp as well as Müler–Israel Stewart mechanisms are employed to formulate the corresponding dynamical and transport equations. We then interlink these evolution equations which help to study the impact of state variables, heat dissipation, modified corrections and charge on the collapse rate. The Weyl scalar is further expressed in terms of the modified field equations. The necessary and sufficient condition of conformal flatness of the considered configuration and homogeneous energy density is obtained by applying some constraints on the model along with disappearing charge and anisotropy. Finally, we discuss different cases to investigate how the spherical matter source is affected by the charge and modified corrections. • We discuss the gravitational collapse of dynamical self-gravitating fluid distribution. • We assume a charged anisotropic spherical geometry involving dissipation flux. • The necessary and sufficient condition of conformal flatness and homogeneous energy density is obtained. • We discuss different cases how the spherical matter source is affected by the charge and modified corrections.

Rapidly rotating self-gravitating Boussinesq fluid. III. A previously unknown zonal oscillation at the onset of rotating convection

Rotating convection in spheres or spherical shells has been modeled in order to understand dynamics in planetary or stellar interiors. Existing theories have predicted various different types of symmetry for the dynamics at the onset of thermal convection. The only form of global convection not found so far is axisymmetric and equatorially symmetric. In this Letter, we for the first time, report the discovery of a solution bearing such symmetry. It is the geometric oblateness due to rotational flattening that is the key factor, which had not previously been considered.

Hölder Space Theory for the Rotation Problem of a Two-Phase Drop

We investigate a uniformly rotating finite mass consisting of two immiscible, viscous, incompressible self-gravitating fluids which is governed by an interface problem for the Navier–Stokes system with mass forces and the gradient of the Newton potential on the right-hand sides. The interface between the liquids is assumed to be closed. Surface tension acts on the interface and on the exterior free boundary. A study of this problem is performed in the Hölder spaces of functions. The global unique solvability of the problem is obtained under the smallness of the initial data, external forces and rotation speed, and the proximity of the given initial surfaces to some axisymmetric equilibrium figures. It is proved that if the second variation of the energy functional is positive and mass forces decrease exponentially, then small perturbations of the axisymmetric figures of equilibrium tend exponentially to zero as the time t→∞, and the motion of liquid mass passes into the rotation of the two-phase drop as a solid body.

Bifurcations to quasiperiodicity of the torsional solutions of convection in rotating fluid spheres: Techniques and results

The linear stability of the periodic and axisymmetric solutions of the convection in rotating, internally heated, and self-gravitating fluid spheres is presented. The transition to quasiperiodic flows via Neimark–Sacker bifurcations of different azimuthal wave numbers, m, is studied using matrix-free continuation and Floquet theory. Several pairs of Ekman and Prandtl numbers are considered in the region where the first bifurcation from the conduction state gives rise to the axisymmetric solutions. It is shown that the azimuthal wave numbers m = 1 and m = 2 are preferred and that, for small Ekman and Prandtl numbers, the secondary bifurcations to different m accumulate close to the onset of convection. This study confirms some results previously found just by direct simulations. The methods presented can be applied to systems of parabolic partial differential equations with O(2) or SO(2) symmetry group, when a periodic orbit, invariant under the group, loses stability through a Neimark–Sacker bifurcation.

Rapidly rotating self-gravitating Boussinesq fluid. II. Onset of thermal inertial convection in oblate spheroidal cavities

For decades researchers have been studying the problem of thermal instabilities in rotating spheres or spherical shells. A key assumption is that the geometrical flattening due to centrifugal force can be neglected, which seems to be a good approximation for many planets and stars. However, this has never been tested. In this paper, the linear stability onset problem at low Prandtl number is considered in oblate spheroids, whose shapes are consistent with figure theory, and it is compared with the previously known spherical system solutions.

Density distribution function of a self-gravitating isothermal turbulent fluid in the context of molecular cloud ensembles – III. Virial analysis

ABSTRACT In this work, we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov & Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not only for supersonic flows but for trans- and subsonic ones as well. Making use of the Eulerian virial theorem at an arbitrary scale, far from the cloud core, we derive an equation for the density profile and solve it in approximate way. The result confirms the solution ϱ(ℓ) = ℓ−2 found in the previous papers. This solution corresponds to three possible configurations for the energy balance. For trans- or subsonic flows, we obtain a balance between the gravitational and thermal energy (Case 1) or between the gravitational, turbulent, and thermal energies (Case 2) while for supersonic flows, the possible balance is between the gravitational and turbulent energy (Case 3). In Cases 1 and 2, the energy of the fluid element can be negative or zero; thus the solution is dynamically stable and shall be long lived. In Case 3, the energy of the fluid element is positive or zero, i.e. the solution is unstable or at best marginally bound. At scales near the core, one cannot neglect the second derivative of the moment of inertia of the gas, which prevents derivation of an analytic equation for the density profile. However, we obtain that gas near the core is not virialized and its state is marginally bound since the energy of the fluid element vanishes.

A measure of complexity for axial self-gravitating static fluids

One of the feasible potential candidates for illustrating the accelerating expansion of the cosmos can be taken through the notion of modified gravity. Within the context of metric f(R) gravity, the contribution of this work features a better understanding of complexity factors for anisotropic static fluid composition in axially symmetric spacetime. This is a generalization of the work done by Herrera et al (2019, Phys. Rev. D 99, 044 049). We formulate generalized dynamical and field equations for anisotropic sources in our analysis. We will compute three distinct complexity factors (Y TF1, Y TF2, Y TF3) after incorporating structure scalars via orthogonal breakdown of the curvature tensor. The differential equations for the conformal tensor are assessed in terms of these complexity factors for the physical illustration. It is inferred that all these factors vanish for the matter spheroid provided with energy homogeneity and isotropic pressure. Nonetheless, the vanishing of these factors might be observed in different scenarios. This happened because energy inhomogeneity and pressure anisotropy cancel out each other in the description of complexity factors. Certain exact solutions of this nature have been reported and studied. All of the outcomes would reduce to general relativity within usual limits.

Dissipative charged homologous model for cluster of stars in f(R,T) gravity

In this paper, we discuss homologous model for cluster of stars in f ( R , T ) gravity. For this purpose, we use f ( R , T ) = R + K ( − T ) n model to incorporate exotic terms in the system. The quasi-static approximations are being imposed onto the shear-free dissipative relativistic self-gravitating charged fluid. It is found that non-dissipative case can easily be reduced to linear homology law in the Newtonian regime. In dissipative scenario, this condition exhibits that the linear homology law for a fluid element is applicable only if we apply the homology conditions on temperature, emission rate and charge associated to baryonic matter. For dark matter, it depends upon the emission of gravitational dissipation. We also deduce that the shear-free and homogeneous expansion rate conditions are equivalent to the homology conditions only in the Newtonian limit. Furthermore, the deviation from homology conditions leads to thermal peeling effects. We use PSR J 1614 − 2230 data with f ( R , T ) field equations for which the graphical analysis shows that the physical variables of baryonic matter like density, pressures and dissipation are suppressed in the presence of dark matter. Thus dark matter has a significant relevance in the emergence of homologous evolution of stellar cluster.

Implications for vanishing complexity in dynamical spherically symmetric dissipative self-gravitating fluids

The complexity factor, originally based on a probabilistic description of a physical system, was re-defined by Herrera et al. for relativistic systems. This involves an assessment of the energy density inhomogeneity, anisotropic and shear stresses, and in the case of radiating collapse, the effects of heat flux. Already well integrated into the modelling of static configurations, the complexity factor is now being studied with respect to dynamical, self-gravitating systems. For static systems, the constraint of vanishing complexity is typically used however for the non-static case, the physical viability of the vanishing condition is less clear. To this end, we consider the ideal case of vanishing complexity in order to solve for the time-dependent gravitational potentials and generate models. We find that vanishing complexity constrains the metric to be of a form similar to that of Maiti’s conformally flat metric.

Existence of energy density homogeneity for radiating spheres in f ( G , T ) gravity

This work discusses the responsible quantities of the emergence inhomogeneity by taking locally anisotropic radiating fluid in [Formula: see text] theory, where T and [Formula: see text] indicate the trace of stress energy tensor and Gauss–Bonnet terms. The temporal and radial change in mass function is observed with the help of a modified version of Einstein’s field equations. To observe the dynamics of self-gravitating fluid, the dynamical equations and differential equations for conformal tensor are constructed, which help to understand the role of correction terms, Weyl curvature, and fluid parameter in the energy–density irregularity. Various forms of fluid are addressed to meet the desired results.

Rapidly rotating self-gravitating Boussinesq fluid: A nonspherical model of motionless stable stratification

A rotating fluid planet or star is nonspherical due to the centrifugal force. However, existing models commonly used an inconsistent spherical approximation, neglecting the flattening. People have found that a baroclinic torque results, which can drive differential rotation, meridional circulation, and turbulence. But the realistic nonspherical geometry, as depicted by the white dashed line, naturally avoids the unreal baroclinicity.

Complexity factor for black holes in the framework of the Newman–Penrose formalism

In this work, we introduce the complexity factor in the context of self-gravitating fluid distributions for the case of black holes by employing the Newman–Penrose formalism. In particular, by working with spherically symmetric and static AdS black holes, we show that the complexity factor can be interpreted in a natural way at the event horizon. Specifically, a thermodynamic interpretation for the aforementioned complexity factor in terms of a pressure partially supporting a Van der Waals-like equation of state is given.

Methods for relativistic self-gravitating fluids: from binary neutron stars to black hole-disks and magnetized rotating neutron stars

The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short \(\gamma \)-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modeling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium and quasiequilibrium solutions for three astrophysically relevant relativistic, self-gravitating fluid systems: Binary neutron stars, black hole-disks, and magnetized rotating neutron stars. These solutions are necessary not only for modeling such compact objects, but equally important, for providing self-consistent initial data in numerical relativity simulations. Instead of presenting the full details of the formulations and numerical algorithms, we focus on painting the broadbrush picture of the methods developed to address these problems, and facilitate future work in the area.

Charged Shear-Free Fluids and Complexity in First Integrals.

The equation is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein–Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for and in terms of elementary and special functions. The explicit forms and arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral.

Nonideal self-gravity and cosmology: Importance of correlations in the dynamics of the large-scale structures of the Universe

Aims. Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for small-scale inhomogeneities in self-gravitating astrophysical fluids by deriving a nonideal virial theorem and nonideal Navier-Stokes equations. These equations involve the pair radial distribution function (similar to the two-point correlation function used to characterize the large-scale structures of the Universe), similarly to the interaction energy and equation of state in liquids. Within this framework, small-scale correlations lead to a nonideal amplification of the gravitational interaction energy, whose omission leads to a missing mass problem, for instance, in galaxies and galaxy clusters. Methods. We propose to use a decomposition of the gravitational potential into a near- and far-field component in order to account for the gravitational force and correlations in the thermodynamics properties of the fluid. Based on the nonideal virial theorem, we also propose an extension of the Friedmann equations in the nonideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe. Results. We estimate that the nonideal amplification factor of the gravitational interaction energy of the baryons lies between 5 and 20, potentially explaining the observed value of the Hubble parameter (since the uncorrelated energy accounts for ∼5%). Within this framework, the acceleration of the expansion emerges naturally because the number of substructures induced by gravitational collapse increases, which in turn increases their contribution to the total gravitational energy. A simple estimate predicts a nonideal deceleration parameter qni ≃ −1; this is potentially the first determination of the observed value based on an intuitively physical argument. We also suggest that small-scale gravitational interactions in bound structures (spiral arms or local clustering) could yield a transition to a viscous regime that can lead to flat rotation curves. This transition could also explain the dichotomy between (Keplerian) low surface brightness elliptical galaxy and (nonkeplerian) spiral galaxy rotation profiles. Overall, our results demonstrate that nonideal effects induced by inhomogeneities must be taken into account, potentially with our formalism, in order to properly determine the gravitational dynamics of galaxies and the large-scale Universe.

Beltrami–Bernoulli equilibria in weakly rotating self-gravitating fluid

In the presence of a stationary gravitomagnetic field, a weakly rotating self-gravitating fluid relaxes into equilibrium flow configurations which admit both large- and small-scale structures. Unlike the traditional Beltrami equilibria in fluid, the equilibrium states in a rotating self-gravitating fluid in a gravitomagnetic field have structure similar to that of double curl Beltrami equilibria in plasma where the generalized vortical lines are aligned with the flow field. Different equilibrium flow configurations in the rotating fluid can be distinguished by the ratio between total energy and helicity. However, these fluid equilibria do not exhibit diamagnetic behaviours as observed in multi-species plasma equilibria.

On the study of complexity for charged self-gravitating systems

In modified Gauss–Bonnet gravity, this paper investigates the complexity factor for static anisotropic self-gravitating fluid which is influenced by an electric charge. For the self-gravitating system, we evaluate the Maxwell field equations, the Tolman–Oppenheimer–Volkoff equation and the mass function. We formulate the structure scalars by an orthogonal splitting of the Riemann tensor for the self-gravitating system and identify one of these scalars as the complexity factor. Then with the help of two different models, we observe the corresponding complexity factor involved in the subsequent changes of static spheres. The structure scalars and complexity factor are found to be dependent on the components of the effective part as well as electromagnetic part.

Tolman-Ehrenfest-Klein law in non-Riemannian geometries

Heat always flows from hotter to a colder temperature until thermal equilibrium be finally restored in agreement with the usual (zeroth, first and second) laws of thermodynamics. However, Tolman and Ehrenfest demonstrated that the relation between inertia and weight uniting all forms of energy in the framework of general relativity implies that the standard equilibrium condition is violated in order to maintain the validity of the first and second law of thermodynamics. Here we demonstrate that the thermal equilibrium condition for a static self-gravitating fluid, besides being violated, is also heavily dependent on the underlying spacetime geometry (whether Riemannian or non-Riemannian). As a particular example, a new equilibrium condition is deduced for a large class of Weyl and f(R) type gravity theories. Such results suggest that experiments based on the foundations of the heat theory (thermal sector) may also be used for confronting gravity theories and prospect the intrinsic geometric nature of the spacetime structure.

Weak-strong uniqueness principle for compressible barotropic self-gravitating fluids

The aim of this work is to prove the weak–strong uniqueness principle for the compressible Navier–Stokes–Poisson system on an exterior domain, with an isentropic pressure of the type p(ϱ)=aϱγ and allowing the density to be close or equal to zero. In particular, the result will be first obtained for an adiabatic exponent γ∈[9/5,2] and afterwards, this range will be slightly enlarged via pressure estimates “up to the boundary”, deduced relaying on boundedness of a proper singular integral operator.

Complexity factor for anisotropic self-gravitating sphere in Rastall gravity

This paper investigates the new definition of complexity factor for the case of irrotational spherical relativistic structure in the Rastall theory of gravity (RTG). To do so, we assumed static spherically symmetric metric with anisotropic self-gravitating fluid. We studied Rastall field equations, generalized nonconservation equation, mass function and physical impacts of Rastall parameter [Formula: see text] on various material variables by employing certain observational data of compact objects like PSR J1614-2230, 4U1608-52, SAX J 1808.4-3658, 4U1820-30 and Vela X-1. We obtained structure scalars through orthogonal decomposition of the curvature tensor and then utilize these scalars to find the complexity factor of the self-gravitating spherical structure. We examined that the vanishing complexity factor condition is an effective energy density inhomogeneity and an effective anisotropy of pressure which must cancel each other, employed the condition [Formula: see text]. Moreover, we also depicted the solutions of interior formation of spherical stellar object regarding to this vanishing complexity condition. Finally, it is found that the complexity of the system enhances due to the presence of nonminimal to curvature matter couple parameter [Formula: see text]. It is very fascinating to report here that these outcomes could be recovered back to former solutions about complexity factor in General Relativity (GR) by imposing [Formula: see text].