Narrow Results

The fluid-dynamical model of a self-gravitating mass of viscous liquid with singular density at the center vibrating in fundamental mode is considered in juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass of incompressible inviscid liquid. Particular attention is given to the difference between spectral formulas for the frequency and lifetime of f-mode in the singular and homogeneous models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stage of red giants and stellar cocoons — spherical gas-dust clouds with dense star-forming core at the center.

Bekenstein has obtained an upper limit on the entropy S, and from that, an information number bound N is deduced. In other words, this is the information contained within a given finite region of space that includes a finite amount of energy. Similarly, this can be thought as the maximum amount of information required to perfectly describe a given physical system down to its quantum level. If the energy and the region of space are finite then the number of information N required in describing the physical system is also finite. In this short paper, two information number bounds are derived and compared for two types of universe. First, a universe without a cosmological constant Λ and second a universe with a cosmological constant Λ are investigated. This is achieved with the derivation of two different relations that connect the Hubble constant and cosmological constants to the number of information N. We find that the number of information N involved in the two universes are identical or N₂ = N_2Λ, and that the total mass of the universe scales as the square root of the information number N, containing. an information number N of the order of 10¹²². Finally, we expressed Calogero's quantization action as a function of the number of information N. We also have found that in self-gravitating systems the number of information N in nats is the ratio of the total kinetic to total thermal energy of the system.

This paper explores some wormhole (WH) solutions in the background of additional matter contents of f(R, T) modified gravity. For this purpose, we have considered WH geometry filled with two physically different fluid configurations: one is anisotropic and another is anisotropic characterized by the barotropic equation of state. The energy conditions are examined with particular modified gravity model and found the existence of WH solutions even in the absence of exotic matter. Also, we have analyzed the behavior of shape function in this framework. The stability and physical existence of these solutions is studied with different fluid configurations. We conclude that in the absence of exotic matter, one can find WH solutions with particular model of modified gravity.

Assuming a system with spherical symmetry in f(R) gravity filled with dissipative charged and anisotropic matter, we study the impact of density inhomogeneity and local anisotropy on the gravitational collapse in the presence of charge. For this purpose, we evaluated the modified Maxwell field equations, Weyl curvature tensor, and the mass function. Using Misner–Sharp mass formalism, we construct a relation between the Weyl tensor, density inhomogeneity, and local anisotropy. Specifically, we obtain the expression of modified Tolman mass which helps to analyze the influence of charge and dark source terms on different physical factors, also it helps to study the role of these factors on gravitational collapse.

In this paper, we study the importance of configurations of the observer’s congruences in the analysis of the dynamical properties of planar relativistic systems in f(R) geometry. To this end, we assume a relativistic distribution of matter contents whose gravitational effects would produce planar geometry. In order to relate matter ingredients seen by tilted and non-tilted observers, we have calculated particular theoretical relationships. After calculating dynamical, Ellis and transport equations, the pace of gravitational collapse as well as the corresponding stable epochs of the systems are discussed. The instability of non-comoving reference frame has been elaborated in a particular background.

The purpose of this paper is to formulate a complexity factor for a non-static cylindrical structure in the background of $f(G,T)$ gravity, where $G$ and $T$ represent the Gauss–Bonnet term and trace of the energy–momentum tensor, respectively. Different physical factors such as inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms are considered as candidates of complexity. In order to determine a complexity factor encompassing the essential aspects of the system, we apply the technique of orthogonal splitting to the Riemann tensor. We also study evolution of the cylinder through two modes: homologous and homogeneous. Further, we utilize the complexity-free and homologous conditions to examine the dissipative and non-dissipative self-gravitating system. Finally, the factors responsible for inducing complexity during the evolution system are inspected. We deduce that the modified terms in $f(G,T)$ gravity make the system more complex.

In this paper, we investigate how the electromagnetic field influences the idea of complexity within the framework of squared gravity. The physical traits, including heat dissipation, charge, anisotropic pressure, energy density variations and correction components are found to be significant contributors of complexity in celestial objects. By employing Herrera’s orthogonal splitting approach, scalar functions are obtained yielding a complexity factor that incorporates the crucial attributes of the self-gravitating system. Furthermore, we examine the dynamics of charged spherical configuration by considering homologous mode as the simplest evolutionary pattern. Our investigation includes complexity-free scenarios (dissipative/non-dissipative) with homologous constraints. Moreover, we explore the components that contribute toward complexity during the evolutionary process. We conclude that self-gravitating structures get more complex with the inclusion of extra curvature terms of squared gravity and charge.

The statistical mechanics of collisionless self-gravitating systems is a longstanding puzzle, which has not yet been successfully solved. We performed preliminary investigations and then formulated a framework of the entropy-based equilibrium statistical mechanics for collisionless self-gravitating systems. This theory is based on the Boltzmann–Gibbs entropy and includes the generalized virial equations as additional constraints. With the truncated distribution function to the lowest order, we derived a set of second-order equations for the equilibrium states of the system, and solved the numerical solutions of these equations. It is found that there are three types of solutions for these equations. Both the isothermal and divergent solutions are thermally unstable and have unconfined density profiles with infinite mass, energy and spatial extent. The convergent solutions, however, seem to be reasonable. These solutions are just the lowest-order approximation, but they have already manifested the qualitative success of our theory. The second-order variations of the entropy functional indicate that the stationary solutions are neither maximum nor minimum, but saddle-point solutions. Inspired by the saddle-point solutions, we distinguish between two types of perturbations in self-gravitating systems, namely, the large-scale mass perturbation and the small-scale density perturbation, which correspond to long-range violent relaxation and short-range relaxation/Landau damping, respectively, which operate in different fashions. This result is consistent with Antonov's proof, or Binney's argument, that there are no global maximum entropy states for self-gravitating systems. These investigations indicate the achievements that we have made towards this long-standing unsolved problem on the statistical mechanics of self-gravitating systems.

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2, the spacetime has plane symmetry.

The decreasing of the inertial mass density, established in the past for dissipative fluids, is found to be produced by the "inertial" term of the transport equation. Once the transport equation is coupled to the dynamical equation, one finds that the contribution of the inertial term diminishes the effective inertial mass and the "gravitational" force term, by the same factor. An intuitive picture and prospective applications of this result to astrophysical scenarios are discussed.

We study an isothermal system of semi-degenerate self-gravitating fermions in general relativity (GR). The most general solutions present is mass density profiles with a central degenerate compact core governed by quantum statistics followed by an extended plateau, and ending in a power law behavior r^-2. By fixing the fermion mass m in the keV regime, the different solutions depending on the free parameters of the model: the degeneracy and temperature parameters at the center, are systematically constructed along the one-parameter sequences of equilibrium configurations up to the critical point, which is represented by the maximum in a central density (ρ₀) versus core mass (M_c) diagram. We show that for fully degenerate cores, the Oppenheimer–Volkoff (OV) mass limit is obtained, while instead for low degenerate cores, the critical core mass increases showing the temperature effects in a nonlinear way. The main result of this work is that when applying this theory to model the distribution of dark matter (DM) in big elliptical galaxies from miliparsec distance-scales up to 10² Kpc, we do not find any critical core-halo configuration of self-gravitating fermions, able to explain both the most super-massive dark object at their center together with the DM halo simultaneously.

This paper investigates the effects of dark source term on the dissipative axially symmetric collapse by taking self-interacting Brans–Dicke (SBD) gravity as a dark energy (DE) candidate. We discuss physically feasible energy source of the model and formulate all the dynamical variables as well as structure scalars. It is found that the dark source term is one of the source of anisotropy and dissipation in the system. Further, we obtain structure scalars in this background. In order to discuss factors describing dissipative collapse, we develop equations related to the evolution of dynamical variables, heat transport equation as well as super-Poynting vector. We conclude that the thermodynamics of the collapse, evolution of kinematical terms (like expansion scalar, shear and vorticity) and inhomogeneity are affected by dark source term. Finally, we study the existence of radiation having repulsive gravitational nature in this collapse scenario.

We investigate the role of tilted and nontilted congruence in the dynamics of dissipative Lemaître–Tolman–Bondi spacetime in $f(R,T)$ gravity. We consider imperfect fluid with its congruences observed by tilted observer and dust fluid filled with LTB geometry observed by the nontilted observer. In order to elaborate the dynamical features of two congruences, we consider well-known $f(R,T)$ models and develop relationships between tilted and nontilted dynamical variables. We evaluate the nonzero divergence of energy–momentum tensor for tilted congruence and transport equation for the system in $f(R,T)$ gravity. We have also checked the instability regimes for nontilted congruence.

This paper explores evolution of dissipative axially symmetric collapsing fluid under the dark effects of $f(G)$ gravity. We formulate the dynamical variables and study the effects of dark sources in pressure anisotropy as well as heat dissipation. The structure scalars (scalar functions) as well as their role in the dynamics of source are investigated. Finally, we develop heat transport equation to examine the thermodynamic aspect and a set of equations governing the evolution of dynamical variables. It is concluded that dark sources affect thermodynamics of the system, evolution of kinematical quantities as well as density inhomogeneity.

In this work, we attempt to generalize the statistical mechanics of self-gravitating systems to systems consisting of two species gravitating particles. Under the nondegenerate condition, with the second-order approximation, and with virialization relationships as additional constraints, we obtain the entropy expression for the two species system. Then, by extremizing the constrained entropy with variational calculus, we obtain a series of equations to describe the equilibrium states of the system. Under the assumption that there is no difference of velocity distributions between the two species, from the series of equilibrium-state equations, we obtain the relative ratio of the spatial distributions for the two species. The two species may be mixed homogeneously in space, yet with different choices of the relevant parameters $h_1$ and $h_2$, two Lagrangian multipliers in the statistical equilibrium equations, their spatial distributions may also differ from each other. The deviation of the spatial distributions between the two species is usually explained as mass segregation, which is confirmed by recent observations in some Galactic stellar clusters. We emphasis, however, that the mass segregation here is not caused by kinetic-energy exchange between the two species, but a new feature of our statistical approach, which is different from Lynden-Bell’s statistics. We believe that these results may have general significance to the statistical mechanics for the general long-range interaction systems.

We analyze the intriguing possibility of explaining both dark mass components in a galaxy: the dark matter (DM) halo and the supermassive dark compact object lying at the center, by a unified approach in terms of a quasi-relaxed system of massive, neutral fermions in general relativity. The solutions to the mass distribution of such a model that fulfill realistic halo boundary conditions inferred from observations, develop a high-density core supported by the fermion degeneracy pressure able to mimic massive black holes at the center of galaxies. Remarkably, these dense core-diluted halo configurations can explain the dynamics of the closest stars around Milky Way’s center (SgrA*) all the way to the halo rotation curve, without spoiling the baryonic bulge-disk components, for a narrow particle mass range $m{c}^2\sim 10$–$10^2$keV.

In this paper, we extend the notion of complexity for the case of nonstatic self-gravitating spherically symmetric structures within the background of modified Gauss–Bonnet gravity (i.e. $f(G)$ gravity), where $G$ denotes the Gauss–Bonnet scalar term. In this regard, we have formulated the equations of gravity as well as the relations for the mass function for anisotropic matter configuration. The Riemann curvature tensor is broken down orthogonally through Bel’s procedure to compose some modified scalar functions and formulate the complexity factor with the help of one of the scalar functions. The CF (i.e. complexity factor) comprehends specific physical variables of the fluid configuration including energy density inhomogeneity and anisotropic pressure along with $f(G)$ degrees of freedom. Moreover, the impact of the dark source terms of $f(G)$ gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms.

We study the nonlinear structure formation in cosmology accounting for the quantum nature of the dark matter (DM) particles in the initial conditions at decoupling, as well as in the relaxation and stability of the DM halos. Different from cosmological N-body simulations, we use a thermodynamic approach for collisionless systems of self-gravitating fermions in general relativity, in which the halos reach the steady state by maximizing a coarse-grained entropy. We show the ability of this approach to provide answers to crucial open problems in cosmology, among others: the mass and nature of the DM particle, the formation and nature of supermassive black holes in the early Universe, the nature of the intermediate mass black holes in small halos, and the core-cusp problem.

In this work, we focus on constructing two analogs of an anisotropic seed solution via the decoupling technique. For this purpose, we add a new matter source alongside the anisotropic fluid in a static sphere. A transformation in the radial metric component is applied to split the field equations into two sets such that the influence of each source is limited to one array. The anisotropic solution constructed by employing the embedding class-one condition is used to specify the set corresponding to the seed source. We obtain two solutions of the second set (related to the additional source) by applying constraints on the anisotropy and complexity of the self-gravitating system. A smooth junction between the interior and exterior spacetimes determines the unknown constants. Various physical characteristics, such as viability and stability, are graphically analyzed by utilizing the radius and mass of the star PSR J1614-2230. It is found that the extended solutions agree with the energy conditions as well as stability criteria for selected values of the parameters.

In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f({ℛ},{𝒯},{{ℛ}}_{\gamma \chi }{{𝒯}}^{\gamma \chi })$ gravity, where ${ℛ}$ and ${𝒯}$ indicate the Ricci scalar and trace of the energy–momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $\xi$. The first set is associated with isotropic distribution, i.e. modified Krori–Barua solution. The second set is influenced from anisotropic factor and contains unknowns which are determined by taking some constraints. The impact of decoupling parameter is then analyzed on the obtained physical variables and anisotropy. We also investigate energy conditions and some other parameters such as mass, compactness and redshift graphically. It is found that our solution corresponding to pressure-like constraint shows stable behavior throughout in this gravity for the considered range of $\xi$.