Inhomogeneous Energy Density Research Articles

Influence of modification of gravity on the complexity factor of static spherical structures

ABSTRACT The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in f (R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy–momentum tensor, and Q ≡ RαβT αβ. In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f (R, T, Q) = R condition.

Effects of electromagnetic field on the structure of massive compact objects

This paper encompasses a set of stellar equations that administer the formation and evolution of self-gravitating, dissipative spherically symmetric fluid distributions having anisotropic stresses in the presence of electromagnetic field. The Riemann tensor is split orthogonally to procure five scalar functions named as structure scalars which are then utilized in the stellar equations. It is shown that some basic fluid properties such as energy density inhomogeneity, pressure anisotropy and heat flux are interlinked with the obtained scalars. Further, it is shown that all the solutions to Einstein equations can be written in terms of these five scalars keeping in view the static case.

Stability of the isotropic pressure condition

We investigate the conditions for the (in)stability of the isotropic pressure condition in collapsing spherically symmetric, dissipative fluid distributions. It is found that dissipative fluxes, and/or energy density inhomogeneities and/or the appearance of shear in the fluid flow, force any initially isotropic configuration to abandon such a condition, generating anisotropy in the pressure. To reinforce this conclusion we also present some arguments concerning the axially symmetric case. The consequences ensuing our results are analyzed.

Complexity factors for static anisotropic axially symmetric fluid distributions in f(R) gravity

In this paper, we have analyzed the complexity factor for the most general axially symmetric static anisotropic fluid distributions in context of [Formula: see text] theory of gravity. For this purpose, we have studied three distinct complexity factors that are organized in terms of three scalar variables (structure scalars) comes from the orthogonal splitting of the curvature tensor. The vanishing of all complexity factors condition for what we choose the simplest fluid distribution that in which system having energy density is homogeneous with isotropic pressure. Although, it has been found that the complexity factors condition can also vanish when inhomogeneous energy density and anisotropy of the pressure cancel each other. Next, we express a class of exact solutions and their graphical analysis as compatible to our models that satisfies the vanishing condition of complexity factors. Finally, it is worth mentioning that these results can reproduce the results of General theory of Relativity under some constraints.

Complexity analysis of dynamical spherically-symmetric dissipative self-gravitating objects in modified gravity

In this paper, we have worked on the concept of complexity factor for nonstatic spherically-symmetric self-gravitating source filled with anisotropic fluid distribution in [Formula: see text] gravity theory. The definition of complexity for dynamical sources, proposed by Herrera, is examined in the framework of [Formula: see text] gravity. We intended to analyze the behavior of complexity factor in modified theory. For this, we defined the scalar functions through orthogonal splitting of Reimann tensor in [Formula: see text] gravity and worked out the structure scalars. We considered the structure scalar [Formula: see text] as a complexity factor to evaluate the complexity of the structure of dynamical system and also to analyze the complexity of the evolutionary patterns of the system under consideration. We took into account the homologous condition and homogeneous expansion condition in order to present the simplest mode of evolution, and found that homologous evolution is the simplest one. We considered both dissipative and nondissipative cases and found that shearing behavior of the fluid is not the same in both cases, however it remained geodesic in both cases. In the end, we established the results for the vanishing of the complexity factor. It has been found that zero complexity condition is satisfied if the energy density inhomogeneity and pressure anisotropy of the fluid configuration cancel each other.

Complexity factors for axially symmetric static sources

A previously found definition of complexity for spherically symmetric fluid distributions [L. Herrera, Phys. Rev. D 97, 044010 (2018).] is extended to axially symmetric static sources. In this case, there are three different complexity factors, defined in terms of three structure scalars obtained from the orthogonal splitting of the Riemann tensor. All these three factors vanish for what we consider the simplest fluid distribution, i.e., a fluid spheroid with isotropic pressure and homogeneous energy density. However, as in the spherically symmetric case, they can also vanish for a variety of configurations, provided the energy density inhomogeneity terms cancel the pressure anisotropic ones in the expressions for the complexity factors. Some exact analytical solutions of this type are found and analyzed. In light of the obtained results, some conclusions about the correlation (the lack of it) between symmetry and complexity are put forward.

Planck 2015 Constraints on the Non-flat XCDM Inflation Model

Abstract We examine the Planck 2015 cosmic microwave background (CMB) anisotropy data by using a physically consistent energy density inhomogeneity power spectrum generated by quantum-mechanical fluctuations during an early epoch of inflation in the non-flat XCDM model. Here dark energy is parameterized using a fluid with a negative equation of state parameter but with the speed of fluid acoustic inhomogeneities set to the speed of light. We find that the Planck 2015 data in conjunction with baryon acoustic oscillation distance measurements are reasonably well fit by a closed-XCDM model in which spatial curvature contributes a percent of the current cosmological energy density budget. In this model, the measured non-relativistic matter density parameter and Hubble constant are in good agreement with values determined using most other data. Depending on cosmological parameter values, the closed-XCDM model has reduced power, relative to the tilted, spatially flat ΛCDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing σ 8 constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. However, the closed-XCDM inflation model does not seem to improve the agreement much, if at all, compared to the closed ΛCDM inflation case, even though it has one additional free parameter.

Complexity factor for anisotropic source in non-minimal coupling metric f(R) gravity

In this outline we recognize the idea of complexity factor for static anisotropic self-gravitating source with generalized f(R) metric gravity theory. In present consideration, we express the Einstein field equations, hydrostatic equilibrium equation, the mass function and physical behavior of f(R) model by using some observational data of well known compact stars like 4U~1820-30, SAX~J1808.4-3658 and Her~X-1. We define the scalar functions through the orthogonal splitting of the Reimann-Christofell tensor and then find the vanishing complexity condition for self-gravitating system with the help of these scalars. It has been found that the vanishing condition for the complexity are pressure anisotropy and energy density inhomogeneity must cancel each other. Moreover, we study the momentous results of an astral object for the vanishing of complexity factor. Finally, these solutions reduced to previous investigation about complexity factor in General Relativity by taking lambda =0.

Planck 2015 Constraints on the Nonflat ϕCDM Inflation Model

Abstract We perform Markov chain Monte Carlo analyses to put constraints on the nonflat ϕCDM inflation model using Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation distance measurements. The ϕCDM model is a consistent dynamical dark energy model in which the currently accelerating cosmological expansion is powered by a scalar field ϕ slowly rolling down an inverse power-law potential energy density. We also use a physically consistent power spectrum for energy density inhomogeneities in this nonflat model. We find that, like the closed-ΛCDM and closed-XCDM models, the closed-ϕCDM model provides a better fit to the lower multipole region of the CMB temperature anisotropy data compared to that provided by the tilted flat-ΛCDM model. Also, like the other closed models, this model reduces the tension between the Planck and the weak lensing σ 8 constraints. However, the higher multipole region of the CMB temperature anisotropy data are better fit by the tilted flat-Λ model than by the closed models.

Independent excitation of inhomogeneous energy density driven instability by electron density gradient

In this work, we report an experimental observation of the inhomogeneous energy density driven instability (IEDDI) independently excited by the electron density gradient. This was achieved using a novel design which could generate a controllable electron density gradient, while the self-consistent electric field accompanied with the electron density gradient can be simultaneously compensated. Broadband wave mode in the ion cyclotron frequency range was excited, which was further experimentally identified as the IEDDI. This result suggests that the IEDDI can be independently excited by the electron density gradient, which could be extended to explain the satellite observations of the broadband extremely low frequency waves in the auroral plasmas where the strong plasma density inhomogeneities exist.

Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model

Abstract We study Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat ΛCDM model. Unlike earlier analyses of non-flat models, which assumed an inconsistent power-law power spectrum of energy density inhomogeneities, we find that the Planck 2015 data alone, and also in conjunction with baryon acoustic oscillation measurements, are reasonably well fit by a closed ΛCDM model in which spatial curvature contributes a few percent of the current cosmological energy density budget. In this model, the measured Hubble constant and nonrelativistic matter density parameter are in good agreement with values determined using most other data. Depending on parameter values, the closed ΛCDM model has reduced power, relative to the tilted, spatially flat ΛCDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing σ 8 constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.

Complexity factor for static anisotropic self-gravitating source in f(R) gravity

In a recent paper, Herrera (Phys Rev D 97:044010, 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 energy density profile and isotropic pressure are capable to diminish their the complexity factor. We are interested to see the effects of f(R) term on complexity factor of the self-gravitating object. The gravitating source with inhomogeneous energy density and anisotropic pressure have maximum value of complexity. Further, such fluids may have zero complexity factor if the effects of inhomogeneity in energy density and anisotropic pressure cancel the effects of each other in the presence of f(R) dark source term. Also, we have found some interior exact solutions of modified f(R) field equations satisfying complexity criterium and some applications of this newly concept to the study of structure of compact objects are discussed in detail. It is interesting to note that previous results about the complexity for static self-gravitating fluid in general relativity can be recovered from our analysis if f(R)=R, which general relativistic limit of f(R) gravity.

Instability Caused by an Inhomogeneous Energy Density Distribution as a Possible Source of Electrostatic Broadband Noise

Plasma instability caused by an inhomogeneous energy density distribution is considered. It is shown that this instability can lead to the excitation of electrostatic ion-cyclotron and oblique ion-acoustic waves, generated in the presence of an inhomogeneous transverse electric field and a shear in the parallel drift velocity of the plasma particles. The considered physical mechanisms of the instability generation in plasma can serve as possible sources of broadband electrostatic turbulence in the auroral ionosphere.

Regularity of intrinsically convex W2,2 surfaces and a derivation of a homogenized bending theory of convex shells

We prove interior regularity for W2,2 isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature.We then derive the Γ-limit of three dimensional nonlinear shells with inhomogeneous energy density, in the bending energy regime. This derivation is incomplete in that it requires an additional technical hypothesis.

Possible Mechanism for Damping of Electrostatic Instability Related to Inhomogeneous Distribution of Energy Density in the Auroral Ionosphere

Satellite observations show that the electrostatic instability, which is expected to occur in most cases due to an inhomogeneous energy density caused by a strongly inhomogeneous transverse electric field (shear of plasma convection velocity), occasionally does not develop inside nonlinear plasma structures in the auroral ionosphere, even though the velocity shear is sufficient for its excitation. In this paper, it is shown that the instability damping can be caused by out-of-phase variations of the electric field and field-aligned current acting in these structures. Therefore, the mismatch of sources of free energy required for the wave generation nearly nullifies their common effect.

New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case

We put forward a new definition of complexity, for static and spherically symmetric self--gravitating systems, based on a quantity, hereafter referred to as complexity factor, that appears in the orthogonal splitting of the Riemann tensor, in the context of general relativity. We start by assuming that the homogeneous (in the energy density) fluid, with isotropic pressure is endowed with minimal complexity. For this kind of fluid distribution, the value of complexity factor is zero. So, the rationale behind our proposal for the definition of complexity factor stems from the fact that it measures the departure, in the value of the active gravitational mass (Tolman mass), with respect to its value for a zero complexity system. Such departure is produced by a specific combination of energy density inhomogeneity and pressure anisotropy. Thus, zero complexity factor may also be found in self--gravitating systems with inhomogeneous energy density and anisotropic pressure, provided the effects of these two factors, on the complexity factor, cancel each other. Some exact interior solutions to the Einstein equations satisfying the zero complexity criterium are found, and prospective applications of this newly defined concept, to the study of the structure and evolution of compact objects, are discussed.

Inflation in a closed universe

To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and non-relativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking's prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wavenumber in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

Electromagnetic effects on the evolution of LTB geometry in modified gravity

We study the influence of Palatini $f(R)$ gravity and tilted observer on the dynamics of Lemaitre–Tolman–Bondi space-time in the presence of electromagnetic field. The imperfect charged fluid seen by tilted observer is considered in comparison with charged dust fluid seen by nontilted observer. We develop the relations between tilted and nontilted variables by including electric charge in Palatini $f(R)$ gravity. In this framework, we explore the evolution of energy density inhomogeneities for tilted and nontilted observers by calculating the energy conservation laws for charged fluid. Finally, we evaluate a constraint on the electric charge in the collapse of stellar objects, which leads to the instability of nontilted congruence.

Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model.

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.

Causes of irregular energy density inf(R,T)gravity

We investigate irregularity factors for a self-gravitating spherical star evolving in the presence of imperfect fluid. We explore the gravitational field equations and the dynamical equations with the systematic construction in $f(R,T)$ gravity, where $T$ is the trace of the energy-momentum tensor. Furthermore, we analyze two well-known differential equations (which occupy principal importance in the exploration of causes of energy density inhomogeneities) with the help of the Weyl tensor and the conservation laws. The irregularity factors for a spherical star are examined for particular cases of dust, isotropic and anisotropic fluids in dissipative and non-dissipative regimes in the framework of $f(R,T)$ gravity. It is found that as the complexity in the matter with the anisotropic stresses increases, the inhomogeneity factor has more correspondences to one of the structure scalars.