Nonlocal Equation Of State Research Articles

Compact object with a local dark energy shell

We investigate some models of compact objects in the general relativity theory with cosmological constant [Formula: see text], based on two density profiles, one of them attributed to Stewart and the other one to Durgapal and Bannerji, proposed in the literature to model “neutron stars”. For them, a nonlocal equation of state with cosmological constant is obtained as a consequence of the chosen metric. In another direction, we obtain a solution for configurations with null radial pressure. The first model (based on Stewart’s density profile) turned out to be the most interesting, since surprisingly it admits the presence of dark energy in the interior of the star, in the outermost layers, for a certain range of mass–radius ratio [Formula: see text]. This dark energy is independent of the cosmological constant, since it is a consequence of the tangential pressure of the fluid be sufficiently negative. Still in this case, for other values of [Formula: see text], all the energy conditions are satisfied. Another advantage of this model, as well as that based on the density profile of Durgapal and Bannerji, is the existence of intervals of [Formula: see text] compatible with physically acceptable models for [Formula: see text], [Formula: see text] and [Formula: see text], which also allowed us to analyze the influence of [Formula: see text] on the behavior of the fluid with respect to the energy conditions. The other configuration studied here, [Formula: see text], only allows solutions for [Formula: see text], in order to ensure a positive mass for the object and to satisfy all the energy conditions in a specific range of [Formula: see text].

Plausible families of compact objects with a nonlocal equation of state

We present the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. We explore how their physical variables change as the family parameter varies. The models studied correspond to anisotropic spherical matter configurations having a nonlocal equation of state. This particular type of equation of state, with no causality problems, provides at a given point the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in general relativity, we obtain that these models become more potentially stable as the family parameter increases.

Cracking of Self-Gravitating Compact Objects with Local and Non Local Equations of State

We discuss the effect that small fluctuations of density and local anisotropy (principal unequal stresses) may have on the occurrence of cracking in spherical compact objects having a non local and local politropic equations of state. A non local equation of state provides, at a given point, the radial pressure not only as function of the density at that point, but its functional throughout the enclosed distribution. It is shown that departures from the equilibrium may lead to the appearance of cracking and it seams to be related not only to fluctuations on the local anisotropy but also to the density. We have found that these fluctuations should have the same sign and the effect of the perturbations in density qualitatively different to the variations in anisotropy.

The fluctuation-dissipation theorem for contracted descriptions of Markov processes

It is shown that if the Onsager-Casimir relations and the fluctuationdissipation theorem are valid for a stationary, Gaussian, Markov process in anN-dimensional space, then these relations are valid when the process is projected into a subspace of the original space. Both time-reversal-even and time-reversal-odd variables are allowed. Previous derivations of the fluctuation-dissipation theorem for Brownian motion from fluctuating hydrodynamics are special cases of the present result. For the Brownian motion problem, the fluctuation-dissipation theorem is proven for the case of a compressible, thermally conducting fluid with a nonlocal equation of state. Arbitrary slip boundary conditions are considered as well.