scholarly journals Nakedly singular counterpart of Schwarzschild’s incompressible star. A barotropic continuity condition in the center

2019 ◽  
Vol 51 (11) ◽  
Author(s):  
Łukasz Bratek ◽  
Joanna Jałocha ◽  
Andrzej Woszczyna
Keyword(s):  
Energy Density ◽  
Incompressible Fluid ◽  
Equations Of State ◽  
Continuity Condition ◽  
Interior Solution ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Static Sphere ◽  
Proper Energy

Abstract A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vaccuum solution. The solution is a singular counterpart of the Schwarzschild’s interior solution. The initial condition in the center for general barotropic equations of state is established.

scholarly journals Cosmic Evolution of Viscous QCD Epoch in Causal Eckart Frame

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 112
Author(s):  
Eman Abdel Hakk ◽  
Abdel Nasser Tawfik ◽  
Afaf Nada ◽  
Hayam Yassin
Keyword(s):  
Energy Density ◽  
Energy Flow ◽  
Equations Of State ◽  
Temporal Evolution ◽  
Particle Diffusion ◽  
Cosmic Evolution ◽  
Bulk Viscous ◽  
Viscous Pressure ◽  
Bulk Viscous Pressure ◽  
Particle Current

It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density ρ, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter H˙, the cosmic energy density ρ˙, and the share η˙ and the bulk viscous coefficient ζ˙. We also suggest how the bulk viscous pressure Π could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs.

L 1 and L ∞ stability of transition densities of perturbed diffusions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ilya Bitter ◽  
Valentin Konakov
Keyword(s):  
Linear Growth ◽  
Stability Result ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Weak Regularity ◽  
Transition Densities ◽  
The Stability ◽  
Drift Terms

Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.

scholarly journals Cohesive Energy Densities Versus Internal Pressures of Near and Supercritical Fluids

Molecules ◽  
2019 ◽  
Vol 24 (5) ◽  
pp. 961 ◽  
Author(s):  
Michal Roth
Keyword(s):  
Energy Density ◽  
Internal Pressure ◽  
Molar Volume ◽  
Intermolecular Interactions ◽  
Supercritical Fluids ◽  
Cohesive Energy ◽  
Equations Of State ◽  
Reduced Pressure ◽  
Cohesive Energy Density ◽  
Internal Pressures

Over half a century ago, Wiehe and Bagley suggested that a product of the internal pressure and molar volume of a liquid measures the energy of nonspecific intermolecular interactions whereas the cohesive energy reflects the total energy of intermolecular interactions in the liquid. This conjecture, however, has never been considered in connection with near and supercritical fluids. In this contribution, the cohesive energy density, internal pressure and their ratios are calculated from high precision equations of state for eight important fluids including water. To secure conformity to the principle of corresponding states when comparing different fluids, the calculations are carried out along the line defined by equality between the reduced temperature and the reduced pressure of the fluid (Tr = Pr). The results provide additional illustration of the tunability of the solvent properties of water that stands apart from those of other near and supercritical fluids in common use. In addition, an overview is also presented of the derivatives of cohesive energy density, solubility parameter and internal pressure with respect to temperature, pressure and molar volume.

scholarly journals INTERACTING CONSTITUENTS IN COSMOLOGY

2008 ◽  
Vol 17 (06) ◽  
pp. 857-879 ◽  
Author(s):  
R. ALDROVANDI ◽  
R. R. CUZINATTO ◽  
L. G. MEDEIROS
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Source Terms ◽  
Systematic Method ◽  
Usual Approach ◽  
Interaction Terms ◽  
Real Fluids ◽  
Universe Evolution ◽  
Source Fluid

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

scholarly journals Crustal heating in accreting neutron stars from the nuclear energy-density functional theory

2018 ◽  
Vol 620 ◽  
pp. A105 ◽  
Author(s):  
A. F. Fantina ◽  
J. L. Zdunik ◽  
N. Chamel ◽  
J. M. Pearson ◽  
P. Haensel ◽  
...  
Keyword(s):  
Energy Density ◽  
Neutron Stars ◽  
Density Functional ◽  
Equations Of State ◽  
Heat Sources ◽  
Energy Density Functional ◽  
Functional Theory ◽  
X Ray ◽  
Shell Effects ◽  
Nuclear Shell

Context. X-ray observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreted neutron stars. Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts. Aims. The heating in the crust of accreting neutron stars is studied using a fully quantum approach taking consistently into account nuclear shell effects. Methods. To this end, we have followed the evolution of ashes made of 56Fe employing the nuclear energy-density functional theory. Both the outer and inner crusts are described using the same functional, thus ensuring a unified and thermodynamically consistent treatment. To assess the role of accretion on the structure of the crust, we have employed the set of accurately calibrated Brussels–Montreal functionals BSk19, BSk20, and BSk21, for which the equations of state of nonaccreted neutron stars have been already calculated. These energy-density functionals were fitted to the same set of nuclear masses but were simultaneously adjusted to realistic neutron-matter equations of state with different degrees of stiffness at suprasaturation densities. For comparison, we have also considered the SLy4 functional. Results. Due to nuclear shell effects, the interior of fully accreted crust is found to be much less stratified than in previous studies. In particular, large regions of the inner crust contain clusters with the magic number Z = 14. The heat deposited in the outer crust is tightly constrained by experimental atomic mass data. The shallow heating we obtain does not exceed 0.2 MeV per accreted nucleon and is therefore not enough to explain the cooling of some soft X-ray transients. The total heat released in the crust is very sensitive to details of the nuclear structure and is predicted to lie in the range from 1.5 MeV to 1.7 MeV per accreted nucleon. Conclusions. The evolution of an accreted matter element and therefore the location of heat sources are governed to a large extent by the existence of nuclear shell closures. Ignoring these effects in the inner crust, the total heat falls to ∼0.6 MeV per accreted nucleon.

scholarly journals The evolution of high-energy-density physics: From nuclear testing to the superlasers

1997 ◽  
Vol 15 (4) ◽  
pp. 607-626 ◽  
Author(s):  
E. Michael Campbell ◽  
Neil C. Holmes ◽  
Steven B. Libby ◽  
Bruce A. Remington ◽  
Edward Teller
Keyword(s):  
Energy Density ◽  
Equations Of State ◽  
High Energy ◽  
High Energy Density ◽  
Experimental Program ◽  
Hydrodynamic Instabilities ◽  
Next Generation ◽  
Nuclear Testing ◽  
High Energy Density Physics

We describe the role for the next-generation “superlasers” in the study of matter under extremely high-energy-density conditions in comparison with previous uses of nuclear explosives for this purpose. As examples, we focus on three important areas of physics that have unresolved issues that must be addressed by experiment: equations of state, hydrodynamic instabilities, and the transport of radiation. We describe some of the advantages the large lasers will have in a comprehensive, laboratory-based experimental program.

scholarly journals ACCELERATING UNIVERSES WITH SCALING DARK MATTER

2001 ◽  
Vol 10 (02) ◽  
pp. 213-223 ◽  
Author(s):  
MICHEL CHEVALLIER ◽  
DAVID POLARSKI
Keyword(s):  
Dark Matter ◽  
Equation Of State ◽  
Energy Density ◽  
Critical Points ◽  
Equations Of State ◽  
Large Fraction ◽  
Accurate Knowledge ◽  
Friedmann Robertson Walker

Friedmann–Robertson–Walker universes with a presently large fraction of the energy density stored in an X-component with wX<-1/3, are considered. We find all the critical points of the system for constant equations of state in that range. We consider further several background quantities that can distinguish the models with different wXvalues. Using a simple toy model with a varying equation of state, we show that even a large variation of wXat small redshifts is very difficult to observe with dL(z) measurements up to z~1. Therefore, it will require accurate measurements in the range 1<z<2 and independent accurate knowledge of Ωm,0(and/or ΩX,0) in order to resolve a variable wXfrom a constant wX.

scholarly journals New regular black hole solutions and other electrically charged compact objects with a de Sitter core and a matter layer

2018 ◽  
Vol 27 (11) ◽  
pp. 1843015
Author(s):  
Angel D. D. Masa ◽  
Enesson S. de Oliveira ◽  
Vilson T. Zanchin
Keyword(s):  
Black Hole ◽  
Equation Of State ◽  
Energy Density ◽  
Thin Shell ◽  
Compact Objects ◽  
Interior Solution ◽  
De Sitter ◽  
Regular Black Hole ◽  
Electrically Charged ◽  
Black Hole Solutions

The main objective of this work is the construction of regular black hole solutions in the context of the Einstein–Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this purpose, we first write explicitly the Einstein field equations for the interior regular region. We take an electrically charged nonisotropic fluid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure [Formula: see text] is equal to the negative of energy density [Formula: see text], [Formula: see text]. Then, two solutions for the Einstein equations are built, a regular interior solution for the region with matter satisfying a de Sitter equation of state, and an external solution for the region outside the matter, that corresponds to the Reissner–Nordström metric. To complete the solution we apply the Darmois–Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the matching surface is composed by a thin shell of matter, i.e. a surface layer in the form of a perfect fluid obeying a barotropic equation of state, [Formula: see text] and [Formula: see text] being the intrinsic pressure and energy density of the shell, respectively, and [Formula: see text] a constant parameter. We show that there are electrically charged regular black hole solutions and other compact objects for specific choices of [Formula: see text] and of the other parameters of the model. Some properties the objects are investigated.

scholarly journals Scalar and vector perturbations in a universe with nonlinear perfect fluid

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Ezgi Canay ◽  
Ruslan Brilenkov ◽  
Maxim Eingorn ◽  
A. Savaş Arapoğlu ◽  
Alexander Zhuk
Keyword(s):  
Energy Density ◽  
Perfect Fluid ◽  
Nonlinear Equations ◽  
Equations Of State ◽  
Cosmological Models ◽  
Perfect Fluids ◽  
Screening Approach ◽  
Linear And Nonlinear ◽  
Discrete Inhomogeneities

AbstractWe study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.

scholarly journals The relativistic incompressible sphere

1968 ◽  
Vol 8 (1) ◽  
pp. 6-16 ◽  
Author(s):  
H. A. Buchdahl ◽  
W. J. Land
Keyword(s):  
Speed Of Sound ◽  
Interior Solution ◽  
Natural Analogue ◽  
Speed Of Light ◽  
Static Sphere

SummaryThe Schwarzschild Interior Solution represents a static sphere the proper density of which has the same value throughout. Though it is sometimes referred to as an “incompressible” sphere it is physically unacceptable since (formally) the speed of sound within it is infinite. Perhaps the most natural analogue of the classical incompressible sphere is therefore a sphere such that the speed of sound is everywhere just equal to the speed of light. This paper investigates spheres of this kind in some detail.

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