We discuss the gravitational collapse of spherical compact objects in the background of $f(R,T,Q)$ theory, where $R$ represent the Ricci scalar, $T$ is the trace of energy momentum tensor while $Q\equiv R_{μν}T^{μν}$, and investigate the influence of anisotropy and heat dissipation in this scenario. We provide an analysis on the role of distinct material terms considered while studying the dynamical equation. The dynamical equation is coupled with a heat transport equation and discussed in the background of $f(R,T,Q)$ theory of gravity. The reduction element in the density of inertial mass, is re-acquired which is based on the internal position of thermodynamics. In collation with the equivalence relation, the reduction quantity in density is similar as appeared with gravitational force. We formulate the connection of Weyl tensor with different matter variables to see the non-identical outcomes. The inhomogeneous nature of energy density is also analyzed in the framework of modified gravity.
This paper is devoted to study the effects of electromagnetic field on the energy density inhomogeneity in the relativistic self-gravitating fluids for spherically symmetric spacetime. Two important equations of the Weyl tensor are formulated which help to analyze the energy density inhomogeneity in this scenario. We investigate two types of fluids, i.e., non-dissipative and dissipative. The non-dissipative fluid further includes dust, locally isotropic, and locally anisotropic charged fluids. We explore the effects of different factors on energy density inhomogeneity in all these cases, in pa…
We investigate the evolution of self-gravitating either dissipative or non--dissipative systems satisfying the condition of minimal complexity, and whose areal radius velocity is proportional to the areal radius (quasi-homologous condition). Several exact analytical models are found under the above mentioned conditions. Some of the presented models describe the evolution of spherically symmetric dissipative fluid distributions whose center is surrounded by a cavity. Some of them satisfy the Darmois conditions whereas others present shells and must satisfy the Israel condition on either one or …
The shear free condition is studied for dissipative relativistic self-gravitating fluids in the quasi-static approximation. It is shown that, in the Newtonian limit, such condition implies the linear homology law for the velocity of a fluid element, only if homology conditions are further imposed on the temperature and the emission rate. It is also shown that the shear-free plus the homogeneous expansion rate conditions are equivalent (in the Newtonian limit) to the homology conditions. Deviations from homology and their prospective applications to some astrophysical scenarios are discussed, a…
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the structure of the fluid distribution, but also the condition of minimal complexity of the pattern of evolution. As we shall see these two issues are deeply intertwined. For the complexity factor of the structure we choose the same as for the static case, whereas for the simplest pattern of evolution we assume the homologous condition. The dissipative and non-dis…
The Chaplygin gas has been proposed as a possible dark energy, dark matter candidate. As a working fluid in a Friedmann-Robertson-Walker universe, it exhibits early behavior reminiscent of dark matter, but at later times is more akin to a cosmological constant. In any such universe, however, one can expect local perturbations to form. Here we obtain the general equations for a self-gravitating relativistic Chaplygin gas. We solve these equations and obtain the mass-radius relationship for such structures, showing that only in the phantom regime is the mass-radius relationship large enough to b…
In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy density, is taken under consideration. The perturbation scheme is imposed on modified field equations and the dynamical equations. The collapse equation is devised from these perturbed equations which stimulates to disclose the instability zone under both Newtonian and post-Newtonian constraints. It is wrapped up by concluding that dynamical instability is inte…
We develop a general formalism applying to Newtonian self-gravitating Bose-Einstein condensates. This formalism may find application in the context of dark matter halos. We introduce a generalized Gross-Pitaevskii equation including a source of dissipation (damping) and an arbitrary nonlinearity. Using the Madelung transformation, we derive the hydrodynamic representation of this generalized Gross-Pitaevskii equation and obtain a damped quantum Euler equation involving a friction force proportional and opposite to the velocity and a pressure force associated with an equation of state determine…
We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time and the hydrostatic time. It is obtained that the onset of non--equilibrium will critically depend on a single function directly related to the time derivative of the vorticity. Among all fluid variables (at the time scale under consideration), only the tetrad component of the anisotrop…
We identify the factors responsible for the appearance of energy-density inhomogeneities in a self-gravitating fluid, and describe the evolution of those factors from an initially homogeneous distribution. It is shown that a specific combination of the Weyl tensor and/or local anisotropy of pressure and/or dissipative fluxes entails the formation of energy-density inhomogeneities. Different cases are analyzed in detail and in the particular case of dissipative fluids, the role of relaxational processes as well as non-local effects are brought out.
The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal splitting of the Riemann tensor, in the context of general relativity. It is shown that these scalars are directly related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux and the active gravitational mass. It is also shown that in the static case, all poss…
The present work deals with the dynamics of radiating star which is considered to be expansion free cylindrical symmetric dust dissipative fluids. Several treatments are adopted for the description of geometrical and physical features of such stars. Firstly, it is shown that, the dynamical star does not permit the streaming out limit and diffusion approximation and also proved that acceleration and dissipation are necessary for its dynamical evolution. It has also shown that, a static expansion free cylinder must be non-radiating. Secondly, the existence of cavity model and self-similar soluti…
This paper deals with the spherically symmetric self-gravitating star which is considered to be expansion free dissipative perfect fluids distribution. Some recent research reveals that expansion free dynamical star must be accelerating and dissipating. We adopted some conjectures to obtain the analytical solution for the dynamical model of such stars. Firstly, it has shown that density of dynamical star is homogeneous and \Lamada-dominated under quasi-static diffusion approximation. Secondly, the self-similar solution is also discussed to describe the dynamical model.
Using the fact that a spin connection is defined to an accuracy of a vector it is shown that the spin connection should be modified in such a manner that Dirac equation in a curve space would be compatible with Dirac equation in a flat space.
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein coordinates. The simplicity of the system allow to display and deal with the typical gauge instability present in these coordinates. The numerical evolution is performed with a standard method of lines fourth order in space and time. The time algorithm is Runge-Kutta while the space discrete derivative is symmetric (non-dissipative). The constraints are pres…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called $γ$-metric and Erez-Rosen metric with quadrupole moment $q$, influence of the additional deformation parameters $γ_*$ and $q_*$ generated by the scalar field is studied. It is shown that the null energy condition is satisfied for the phantom field, but it is not satisfied for the standard scalar field. The test particle motion in the both modified $γ$-metric …
We study the global stability of a self-gravitating disk in the context of Modified Gravity (MOG) using N-body simulations. This theory is a relativistic scalar-tensor-vector theory of gravity and presented to address the dark matter problem. In the weak field limit MOG possesses two free parameters $α$ and $μ_0$ which have been already determined using rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disk and more specifically the bar instability in MOG is investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface dens…
We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of physical parameters…
This manuscript is devoted to study the combined effect of a viable model, f(R) = R + αR^n, and electromagnetic field on the instability range of gravitational collapse. We assume charged anisotropic fluid that dissipate energy via heat flow and discuss that electromagnetic field, density inhomogeneity, shear and phase transition on astrophysical bodies can be incorporated by locally anisotropic background. Dynamical equations help to investigate the evolution of self-gravitating objects and leads to the conclusion that adiabatic index depend upon the electromagnetic background, mass and radiu…
We study the effective field theory that describes the low-energy physics of self-gravitating media. The field content consists of four derivatively coupled scalar fields that can be identified with the internal comoving coordinates of the medium. Imposing SO(3) internal spatial invariance, the theory describes supersolids. Stronger symmetry requirements lead to superfluids, solids and perfect fluids, at lowest order in derivatives. In the unitary gauge, massive gravity emerges, being thus the result of a continuous medium propagating in spacetime. Our results can be used to explore systematic…
This article focuses on the formulation of some scalar factors which are uniquely expressed in terms of matter variables for dynamical charged dissipative cylindrical geometry in a standard gravity model $\mathcal{R}+Φ\mathcal{Q}$ ($Φ$ is the coupling parameter, $\mathcal{Q}=\mathcal{R}_{φ\vartheta}\mathcal{T}^{φ\vartheta}$) and calculates four scalars by orthogonally decomposing the Riemann tensor. We find that only $\mathcal{Y}_{TF}$ involves inhomogeneous energy density, heat flux, charge and pressure anisotropy coupled with modified corrections, and thus call it as complexity factor for th…
We investigate the role played by density inhomogeneities and dissipation on the final outcome of collapse of a self-gravitating sphere. By imposing a perturbative scheme on the thermodynamical variables and gravitational potentials we track the evolution of the collapse process starting off with an initially static perfect fluid sphere which is shear-free. The collapsing core dissipates energy in the form of a radial heat flux with the exterior spacetime being filled with a superposition of null energy and an anisotropic string distribution. The ensuing dynamical process slowly evolves into a…
The aim of this paper is to explore the complexity factor (CF) for those self-gravitating relativistic spheres whose evolution proceeds non-dynamically. We are adopting the definition of CF mentioned in \cite{PhysRevD.97.044010}, modifying it to the static spherically symmetric case, within the framework of a modified gravity theory (the Palatini $f(R)$ theory). In this respect, we have considered radial dependent anisotropic matter content coupled with spherical geometry and determined the complexity factor involved in the patterns of radial evolution. We shall explore the field and a well-kn…
This paper aims to explore some realistic configurations of anisotropic spherical structures in the background of metric $f(R)$ gravity, where $R$ is the Ricci scalar. The solutions obtained by Krori and Barua are used to examine the nature of particular compact stars with three different modified gravity models. The behavior of material variables is analyzed through plots and the physical viability of compact stars is investigated through energy conditions. We also discuss the behavior of different forces, equation of state parameter, measure of anisotropy and Tolman-Oppenheimer-Volkoff equat…
The imprints of the instantaneous appearance of a conformal Killing vector field on the evolution of self-gravitating fluid spheres
Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca（萨拉曼卡大学基础物理与数学大学研究所）；Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela（委内瑞拉中央大学理学院物理系）；Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca（萨拉曼卡大学应用数学系及基础物理与数学大学研究所）
In this paper, we study the effects of polynomial $f(R)$ model on the stability of homogeneous energy density in self-gravitating spherical stellar object. For this purpose, we construct couple of evolution equations which relate the Weyl tensor with matter parameters. We explore different factors responsible for density inhomogeneities with non-dissipative dust, isotropic as well as anisotropic fluids and dissipative dust cloud. We find that shear, pressure, dissipative parameters and $f(R)$ terms affect the existence of inhomogeneous energy density.
We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such gravitating system. A relation between order parameter and the critical temperature is also established.
The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow…
In a recent paper, Herrera \cite{2} (L. Herrera: Phys. Rev. D97, 044010(2018)) have proposed a new definition of complexity for static self-gravitating fluid in General Relativity. In the present article, we implement this definition of complexity for static self-gravitating fluid to case of $f(R)$ gravity. Here, we found that in the frame of $f(R)$ gravity the definition of complexity proposed by Herrera, entirely based on the quantity known as complexity factor which appears in the orthogonal splitting of the curvature tensor. It has been observed that fluid spheres possessing homogenous ene…
It has been suggested recently to study the dynamics of a gravitating gluon condensate q in the context of a spatially flat Friedmann-Robertson-Walker universe. The expansion of the Universe (or, more generally, the presence of a nonvanishing Ricci curvature scalar R) perturbs the gluon condensate and may induce a nonanalytic term \tilde{h}(R,q) in the effective gravitational action. The aim of this article is to explore the cosmological implications of a particular nonanalytic term \tilde{h} \propto η|R|^{1/2} |q|^{3/4}. With a quadratic approximation of the gravitating gluon-condensate vacuu…
This paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans-Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic pressure and massive scalar field. For this purpose, we formulate structure scalars by orthogonally splitting the Riemann tensor. We show that self-gravitating models collapsing homologously follow the simplest mode of evolution. Furthermore, we demonstrate the effect of scalar field on the complexity and evolution of non-dissipative as well as dissipative syste…
We consider modified $f(R)$ gravity with a kinetic curvature scalar as a chiral self-gravitating model in a spherically symmetric spacetime. Most attention devoted to finding solutions for special case of scaling transformation when modified gravity transforms to Einstein frame from Jordan one. We proposed the method of determination of kinetic function for given scalar field dependence on space coordinate. New classes of solutions are found for special choice of $f(R)$ function.
In this paper, we examine the possible realization of a new family of inflation called "shaft inflation" by assuming the modified Chaplygin gas model and tachyon scalar field. We also consider the special form of dissipative coefficient as $Γ={a_0}\frac{T^{3}}{ϕ^{2 }}$ and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the planes of $n_s - ϕ,~n_s - r$ and $n_s - α_s$ (where $n_s,~α_s,~r$ and $ϕ$ represent spectral index, its running, tensor to scalar ratio and scalar field respec…
We consider the cosmological system with two interacting fluids: dark energy and dark matter, in a homogeneous and isotropic universe with dissipation. The modified gravitational equation for dark matter is solved. The analytic representations for the Little Rip, the Pseudo Rip, and the bounce cosmology models with dissipation are obtained in terms of the thermodynamic parameters in the equation of state. We analyze the corrections in the energy density for dark matter, in view of the dissipative processes and the coupling with dark energy.
We discuss the dynamical analysis in $f(R,T)$ gravity (where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor) for gravitating sources carrying axial symmetry. The self gravitating system is taken to be anisotropic and line element describes axially symmetric geometry avoiding rotation about symmetry axis and meridional motions (zero vorticity case). The modified field equations for axial symmetry in $f(R,T)$ theory are formulated, together with the dynamical equations. Linearly perturbed dynamical equations lead to the evolution equation carrying adiabatic index $Γ$ that defines…
We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coo…
In this article, we have studied a cylindrically symmetric self-gravitating dynamical object via complexity factor which is obtained through orthogonal splitting of Reimann tensor in $f(R,T)$ theory of gravity. Our study is based on the definition of complexity for dynamical sources, proposed by Herrera \cite{12b}. We actually want to analyze the behavior of complexity factor for cylindrically symmetric dynamical source in modified theory. For this, we define the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and work out structure scalars for cylindrical g…
The fluid model for the dark sector of the universe (darkon fluid) introduced previously in \cite{PRD} is reformulated as a modified model involving only variables from physical phase space. The Lagrangian of the model does not possess a free particle limit and hence the particles it describes, darkons, exist only as a self-gravitating fluid. This darkon fluid presents a dynamical realisation of the zero-mass Galilean algebra extended by anisotropic dilational symmetry with dynamical exponent $z=5/3$. The model possesses cosmologically relevant solutions which are identical to those of \cite{P…
Some models of modified gravity and their observational manifestations are considered. It is shown, that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe evolution during the radiation dominated epoch is studied in $R^2$-extended gravity theory. Particle production rate by the oscillating curvature is calculated. Possible implications of the model for cosmological creation of non-thermal dark matter are discussed.
In this paper, we study the dynamics of shearfree dissipative gravitational collapse in modified Gauss-Bonnet theory of gravity - so called f(G) gravity. The field equations of f(G) gravity are applied to shearfree spherical interior geometry of the dissipative star. We formulate the dynamical as well as transport equations and then couple them to investigate the process of collapse. We conclude that the gravitational force in this theory is much stronger as compared to general relativity which indicates increase in the rate of collapse. Further, the relation between the Weyl tensor and matter…
Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the mass density rises with time, the system evolves to the singular state with infinite curvature scalar. The corresponding characteristic time is typically much shorter than the cosmological time.
Thermodynamic compatibility, holographic property and wave-function representation of generalized weakly nonlocal self-gravitating non-relativistic fluids
Budapest University of Technology and Economics（布达佩斯科技经济大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；Society for the Unity of Science and Technology（科学与技术统一协会）
Dynamics and collapse of collisionless self-gravitating systems is described by the coupled collisionless Boltzmann and Poisson equations derived from $f(R)$-gravity in the weak field approximation. Specifically, we describe a system at equilibrium by a time-independent distribution function $f_0(x,v)$ and two potentials $Φ_0(x)$ and $Ψ_0(x)$ solutions of the modified Poisson and collisionless Boltzmann equations. Considering a small perturbation from the equilibrium and linearizing the field equations, it can be obtained a dispersion relation. A dispersion equation is achieved for neutral dus…
We find the dispersion relation for tightly wound spiral density waves in the surface of rotating, self-gravitating disks in the framework of Modified Gravity (MOG). Also, the Toomre-like stability criterion for differentially rotating disks has been derived for both fluid and stellar disks. More specifically, the stability criterion can be expressed in terms of a matter density threshold over which the instability occurs. In other words the local stability criterion can be written as $Σ_0<Σ_{\text{crit}}(v_s,κ,α,μ_0)$, where $Σ_{\text{crit}}$ is a function of $v_s$ (sound speed), $κ$ (epicycl…
Beyond Classical Instability Limits of Anisotropic Self-gravitating Fluid Configurations in Hu-Sawicki Inspired f(R) Gravity
Virtual University of Pakistan（巴基斯坦虚拟大学）；University of Management and Technology（管理科技大学）；Tongji University（同济大学）；King Khalid University（国王哈立德大学）；Zhejiang Normal University（浙江师范大学）
This paper is devoted to the formulation of a complexity factor for dynamical anisotropic sphere in the framework of $f(G,T)$ gravity, where $G$ is the Gauss-Bonnet invariant and $T$ is the trace of energy-momentum tensor. Inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms create complexity within the self-gravitating system. We evaluate the structure scalars by orthogonal splitting of the Riemann tensor to evaluate a complexity factor which incorporates all the fundamental properties of the system. Moreover, we examine the dynamics of the sphere by assumin…
Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other hand this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy betwee…
Starting from the weak field limit, we discuss astrophysical applications of Extended Theories of Gravity where higher order curvature invariants and scalar fields are considered by generalizing the Hilbert-Einstein action linear in the Ricci curvature scalar $R$. Results are compared to General Relativity in the hypothesis that Dark Matter contributions to the dynamics can be neglected thanks to modified gravity. In particular, we consider stellar hydrostatic equilibrium, galactic rotation curves, and gravitational lensing. Finally, we discuss the weak field limit in the Jordan and Einstein f…
We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born-Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell- Boltzmann distribution function $f_0(v)$. Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale le…
