arXiv subjects

Gilberto M. Kremer

Publications and source records attributed to Gilberto M. Kremer.

At least 37 records · Page 2Linked to original sources

arXiv2018

Temperature oscillations of a gas moving close to circular geodesic in Reissner-Nordström spacetime

The objective of this work is to analyze the temperature oscillations that occur in a gas in a circular motion under the action of a Reissner-Nordström gravitational field, verifying the effect of the charge term of the metric on the oscillations. The expression for temperature oscillations follows from Tolman's law written in Fermi normal coordinates for a comoving observer. The motion of the gas is close to geodesic so the equation of geodesic deviation was used to obtain the expression for temperature oscillations. Then these oscillations are calculated for some compact stars, quark stars, black holes and white dwarfs, using values of electric charge and mass from models found in the literature. Comparing the various models analyzed, it is possible to verify that the role of the charge is the opposite of the mass. While the increase of the mass produces a reduction in the frequencies, amplitude and in the ratio between the frequencies, the increase of the electric charge produces the inverse effect. In addition, it is shown that if the electric charge is proportional to the mass, the ratio between the frequencies does not depend on the mass, but only on the proportionality factor between charge and mass. The ratios between the frequencies for all the models analyzed (except for supermassive black holes in the extreme limit situations) are close to the $3/2$ ratio for twin peak quasi-periodic oscillation frequencies, observed in many galactic black holes and neutron star sources in low-mass X-ray binaries.

gr-qc↗

arXiv2018

Relative Entropy of a Freely Cooling Granular Gas

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in the quasi-smooth limit.

cond-mat.soft↗

arXiv2018

Properties of the Homogeneous Cooling State of a Gas of Inelastic Rough Particles

In this work we address the question of whether a low-density system composed of identical rough particles may reach hydrodynamic states (also called \textit{normal} states), even if energy is not conserved in particle collisions. As a way to measure the ability of the system to present a hydrodynamic behavior, we focus on the so-called homogeneous cooling state of the granular gas and look at the corresponding relaxation time as a function of inelasticity and roughness. We report computer simulation results of the sixth- and eighth-order cumulants of the particle velocity distribution function and study the influence of roughness on their relaxation times and asymptotic values. This extends the results of a previous work [Phys. Rev. E \textbf{89}, 020202(R) (2014], where lower-order cumulants were measured. Our results confirm that the relaxation times are not necessarily longer for stronger inelasticities. This implies that inelasticity by itself does not preclude hydrodynamics. It is also observed that the cumulants associated with the angular velocity distribution may reach very high values in a certain region of (small) roughness and that these maxima coincide with small orientational correlation points.

cond-mat.soft↗

arXiv2018

Impact of roughness on the instability of a free-cooling granular gas

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014)], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly degenerate transversal (shear) mode and a longitudinal ("heat") mode are unstable with respect to long enough wavelength excitations. The instability is driven by the shear mode above a certain inelasticity threshold; at larger inelasticity, however, the instability is driven by the heat mode for an inelasticity-dependent range of medium roughness. Comparison with the case of a granular gas of inelastic smooth spheres confirms previous simulation results about the dual role played by surface friction: while small and large levels of roughness make the system less unstable than the frictionless system, the opposite happens at medium roughness. On the other hand, such an intermediate window of roughness values shrinks as inelasticity increases and eventually disappears at a certain value, beyond which the rough-sphere gas is always less unstable than the smooth-sphere gas. A comparison with some preliminary simulation results shows a very good agreement for conditions of practical interest.

cond-mat.soft↗

arXiv2017

Stellar structure model in hydrostatic equilibrium in the context of $f(\mathcal{R})$-gravity

In this work we present a stellar structure model from $f(\mathcal{R})$-gravity point of view capable to describe some classes of stars (White Dwarfs, Brown Dwarfs, Neutron stars, Red Giants and the Sun). This model was based on $f(\mathcal{R})$-gravity field equations for $f(\mathcal{R})= \mathcal{R}+ f_2 \mathcal{R}^2$, hydrostatic equilibrium equation and a polytropic equation of state. We compared the results obtained with those found by the Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge, stellar structure equations undergo modifications. Despite the simplicity of this model, the results were satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This $f(\mathcal{R})$-gravity model has been proved to be necessary to describe stars with strong fields such as White Dwarfs, Neutron stars and Brown Dwarfs, while stars with weaker fields, such as Red Giants and the Sun, were best described by the Newtonian theory.

gr-qc↗

arXiv2017

Cosmological perturbations in transient phantom inflation scenarios

We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era.

gr-qc↗

arXiv2016

Transport coefficients for relativistic gas mixtures of hard-sphere particles

In the present work, we calculate the transport coefficients for a relativistic binary mixture of diluted gases of hard-sphere particles. The gas mixture under consideration is studied within the relativistic Boltzmann equation in the presence of a gravitational field described by the isotropic Schwarzschild metric. We obtain the linear constitutive equations for the thermodynamic fluxes. The driving forces for the fluxes of particles and heat will appear with terms proportional to the gradient of gravitational potential. We discuss the consequences of the gravitational dependence on the driving forces. We obtain general integral expressions for the transport coefficients and evaluate them by assuming a hard-sphere interaction amongst the particles when they collide and not very disparate masses and diameters of the particles of each species. The obtained results are expressed in terms of their temperature dependence through the relativistic parameter which gives the ratio of the rest energy of the particles and the thermal energy of the gas mixture. Plots are given to analyze the behavior of the transport coefficients with respect to the temperature when small variations in masses and diameters of the particles of the species are present. We also analyze for each coefficient the corresponding limits to a single gas so the non-relativistic and ultra-relativistic limiting cases are recovered as well. Furthermore, we show that the transport coefficients have a dependence on the gravitational field.

cond-mat.stat-mech↗

arXiv2016

Thermal Conductivity, Shear and Bulk Viscosities for a Relativistic Binary Mixture

In the present work, we deal with a binary mixture of diluted relativistic gases within the framework of the kinetic theory. The analysis is made within the framework of the Boltzmann equation. We assume that the gas is under the influence of an isotropic Schwarzschild metric and is composed of particles with speeds comparable with the light speed. Taking into account the constitutive equations for the laws of Fourier and Navier-Stokes, we obtain expressions for the thermal conductivity, the shear, and bulk viscosities. To evaluate the integrals we assume a hard-sphere interaction along with non-disparate masses for the particles of each component. We show the analytical expressions and the behavior of the transport coeffcients with respect to a relativistic parameter which gives the ratio of the rest energy of the particles to the thermal energy of the gas.We also determine the dependence of the transport coeffcients with respect to the gravitational potential and demonstrate that the corresponding one component

cond-mat.stat-mech↗

arXiv2016

Analysis of Jeans instability from the Boltzmann equation

The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.

astro-ph.CO↗

arXiv2016

Cosmological model with fermion and tachyon fields interacting via Yukawa-type potential

A model for the universe with tachyonic and fermionic fields interacting through a Yukawa-type potential is investigated. It is shown that the tachyonic field answers for the initial accelerated regime and for the subsequent decelerated regime so that it behaves as an inflaton at early times and as a matter field at intermediate times, while the fermionic field has the role of a dark energy constituent, since it leads to an accelerated regime at later times. The interaction between the fields via a Yukawa-type potential controls the duration of the decelerated era, since a stronger coupling makes a shorter decelerated period.

gr-qc↗

arXiv2016

The van der Waals fluid and its role in cosmology

We analyze the properties of a generic cosmological fluid described by the van der Waals equation of state. Exact solutions for the energy density evolution are found as implicit functions of the scale factor for a flat Friedmann-Robertson-Walker space-time. The possible values of the free parameter in the van der Waals equation are selected \emph{a posteriori}, in accordance with asymptotic behaviors that are physically relevant. The stability of the model against small perturbations is studied through the hydrodynamic perturbations of the fluid for the relevant cases. It is found that a van der Waals fluid seems appropriate to describe non-eternal inflationary scenarios.

gr-qc↗

arXiv2015

Analysis of instability of systems composed by dark and baryonic matter

In this work the dynamics of self-gravitating systems composed by dark and baryonic matter is analyzed. Searching for a description of this dynamics, a system of collisionless Boltzmann equations for the two constituents and the Poisson equation for the gravitational field are employed. Through the solution of these equations the collapse criterion is determined from a dispersion relation. The collapse occurs in an unstable region where the solutions grow exponentially with time. It is shown that the unstable region becomes larger if the dispersion velocity of dark matter becomes larger than the one of the baryonic matter. The results obtained are also compared with the case where only the dark matter is present. The model of the present work has a higher limit of instability and therefore, exhibited an advantage in the structure formation.

astro-ph.CO↗

arXiv2015

Mixtures of relativistic gases in gravitational fields: combined Chapman-Enskog and Grad method and the Onsager relations

In this work we study a r-species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant full Boltzmann equation and we incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the Chapman-Enskog and Grad representations. The thermodynamic fluxes are expressed as functions of the thermodynamic forces so that the generalized expressions for the Navier-Stokes, Fick and Fourier laws are obtained. The constitutive equations for the diffusion and heat fluxes of the mixture are functions of thermal and diffusion forces which depend on the acceleration and the gravitational potential gradient. While this dependence is of relativistic nature for the thermal force, this is not the case for the diffusion forces. We show also that the matrix of the diffusion coefficients is symmetric and the thermal-diffusion coefficient is equal to the diffusion-thermal one, proving the Onsager reciprocity relations. The entropy flux of the mixture is also expressed in terms of the thermal and diffusion forces, so that its dependence on the acceleration and gravitational potential gradient is also determined.

cond-mat.stat-mech↗

arXiv2015

Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field

We investigate a Boltzmann gas at equilibrium with its center of mass moving on a circular geodesics in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the Solar System as well as to strong-field configurations of neutron stars and black holes.

gr-qc↗

arXiv2014

Collisionless self-gravitating systems in f(R)-gravity within Palatini approach and relativistic Boltzmann equation in the Newtonian approach

In this work we analyze the dynamics of collisionless self-gravitating systems described by the f(R)-gravity and Boltzmann equation in the weak field approximation, focusing on the Jeans instability for theses systems. The field equations in this approximation were obtained within the Palatini formalism. Through the solution of coupled equations we achieved the collapse criterion for infinite homogeneous fluid and stellar systems, which is given by a dispersion relation. This result is compared with the results of the standard case and the case for f(R)-gravity in metric formalism, in order to see the difference among them. The limit of instability varies according to which theory of gravity is adopted.

gr-qc↗

arXiv2014

Transport coefficients of a granular gas of inelastic rough hard spheres

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

cond-mat.stat-mech↗

arXiv2014

Fermion field as inflaton, dark energy and dark matter

The search for constituents that can explain the periods of accelerating expansion of the Universe is a fundamental topic in cosmology. In this context, we investigate how fermionic fields minimally and non-minimally coupled with the gravitational field may be responsible for accelerated regimes during the evolution of the Universe. The forms of the potential and coupling of the model are determined through the technique of the Noether symmetry for two cases. The first case comprises a Universe filled only with the fermion field. Cosmological solutions are straightforwardly obtained for this case and an exponential inflation mediated by the fermion field is possible with a non-minimal coupling. The second case takes account of the contributions of radiation and baryonic matter in the presence of the fermion field. In this case the fermion field plays the role of dark energy and dark matter, and when a non-minimal coupling is allowed, it mediates a power-law inflation.

gr-qc↗

arXiv2014

Theory and applications of the relativistic Boltzmann equation

In this work two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external electromagnetic fields in special relativity. In this case the Fourier and Ohm laws are derived and the corresponding transport coefficients are obtained. In the other a relativistic gas under the influence of the Schwarzschild metric is studied. It is shown that the heat flux in Fourier's law in the presence of gravitational fields has three contributions, the usual dependence on the temperature gradient, and two relativistic contributions, one of them associated with an acceleration and another to a gravitational potential gradient. Furthermore it is shown that the transport coefficient of thermal conductivity decreases in the presence of a gravitational field. The dependence of the temperature field in the presence of a gravitational potential is also discussed.

cond-mat.stat-mech↗