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At least 217 records · Page 12Linked to original sources
PubMed2005

On chaotic behavior of gravitating stellar shells.

Motion of two gravitating spherical stellar shells around a massive central body is considered. Each shell consists of point particles with the same specific angular momenta and energies. In the case when one can neglect the influence of gravitation of one ("light") shell onto another ("heavy") shell ("restricted problem") the structure of the phase space is described. The scaling laws for the measure of the domain of chaotic motion and for the minimal energy of the light shell sufficient for its escape to infinity are obtained.

Models, Statistical↗
PubMed2004

Gravitational vacuum condensate stars.

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p(v) = -rho(v) and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness l of fluid with equation of state p = +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k(B)lMc/Planck's over 2 pi, instead of the Bekenstein-Hawking entropy formula, S(BH) = 4 pi k(B)GM(2)/Planck's over 2 pi c. Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

Journal Article↗
PubMed1979

Gravitational interaction of hadrons and leptons: Linear (multiplicity-free) bandor and nonlinear spinor unitary irreducible representations of SL(4R).

We review two possible affine extensions of gravity connected to the strong interactions. In the metric affine theory, torsion and nonmetricity do not propagate, gravitation is effectively unmodified, and the observed approximate conservation of hadron intrinsic hypermomentum-i.e., scaling, SU(6), and Regge trajectories-is due to the GL(4,R) band-spinor structure of the hadrons. In the second approach, the new gravitational Lagrangian density generates propagating but confined torsion and nonmetricity, presumably the main contributions to quark confinement. Leptons are represented nonlinearly as Poincaré spinors with the metric field as "realizer" and Higgs boson, and are unconfined. We present a construction for all linear multiplicity-free (= bandor) representations of GL(4,R) and in particular the [Formula: see text] fitting the hadron manifield. We also construct the Hilbert space hadron states [irreps (irreducible representations) of GA(4,R)] and the nonlinear realizations of GL(4,R) for lepton fields.

Journal Article↗
PubMed1982

Gravitational field of a charged mass point.

Adopting, with Schwarzschild, the Einstein gauge ((munu) = -1), a solution of Einstein's field equations for a charged mass point of mass M and charge Q is derived, which differs from the Reissner-Nordstrøm solution only in that the variable r is replaced by R = (r(3) + a(3))((1/3)), where a is a constant. The Newtonian gravitational potential psi identical with (2/c(2))(1 - g(00)) obeys exactly the Poisson equation (in the R variable), with the mass density equal to (E(2)/4pic(2)), E denoting the electric field. psi also obeys a second linear equation in which the operator on psi is the square root of the Laplacian operator. The electrostatic potential Phi (= Q/R), psi, and all the components of the curvature tensor remain finite at the origin of coordinates. The electromagnetic energy of the point charge is finite and equal to (Q(2)/a). The charge Q defines a pivotal mass M(*) = (Q/G((1/2))). If M < M(*), then the whole mass is electromagnetic. If M > M(*), the electromagnetic part of the mass M(em) equals [M - (M(2) - M(*2))((1/2))], whereas the material part of the mass M(mat) equals (M(2) - M(*2))((1/2)). When M > M(*), the constant a is determined, following Schwarzschild, by shrinking the "Schwarzschild radius" to zero. When M < M(*), a is determined so as to make the gravitational acceleration vanish at the origin.

Journal Article↗
PubMed1999

Scaling the universe: gravitational lenses and the Hubble constant.

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as "gravitational standard rulers" for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Omegao and Lambdao that control the evolution of the volume of the Universe with cosmic time.

Journal Article↗
PubMed2000

Statistics of Dark Matter Halos from Gravitational Lensing.

We present a new approach to measure the mass function of dark matter halos and to discriminate models with differing values of Omega through weak gravitational lensing. We measure the distribution of peaks from simulated lensing surveys and show that the lensing signal due to dark matter halos can be detected for a wide range of peak heights. Even when the signal-to-noise ratio is well below the limit for detection of individual halos, projected halo statistics can be constrained for halo masses spanning galactic to cluster halos. The use of peak statistics relies on an analytical model of the noise due to the intrinsic ellipticities of source galaxies. The noise model has been shown to accurately describe simulated data for a variety of input ellipticity distributions. We show that the measured peak distribution has distinct signatures of gravitational lensing, and its non-Gaussian shape can be used to distinguish models with different values of Omega. The use of peak statistics is complementary to the measurement of field statistics, such as the ellipticity correlation function, and is possibly not susceptible to the same systematic errors.

Journal Article↗
PubMed2000

Detecting the Gravitational Redshift of Cluster Gas.

We examine the gravitational redshift of radiation emitted from within the potential of a cluster. Spectral lines from the intracluster medium (ICM) are redshifted in proportion to the emission-weighted mean potential along the line of sight, amounting to approximately 50 km s-1 at a radius of 100 kpc h-1, for a cluster dispersion of 1200 km s-1. We show that the relative redshifts of different ionization states of metals in the ICM provide a unique probe of the three-dimensional matter distribution. An examination of the reported peculiar velocities of cD galaxies in well-studied Abell clusters reveals that they are typically redshifted by an average of approximately 200 km s-1. This can be achieved by gravity with the addition of a steep central potential associated with the cD galaxy. Note that, in general, gravitational redshifts cause a small overestimate of the recessional velocities of clusters by an average of approximately 20 km s-1.

Journal Article↗
PubMedDate not supplied

Expiratory flow limitation during gravitational drainage of perfluorocarbons from liquid-filled lungs.

Flow limitation during pressure-driven expiration in liquid-filled lungs was examined in intact, euthanized New Zealand white rabbits. The aim of this study was to further characterize expiratory flow limitation during gravitational drainage of perfluorocarbon liquids from the lungs, and to study the effect of perfluorocarbon type and negative mouth pressure on this phenomenon. Four different perfluorocarbons (PP4, perfluorodecalin, perfluoro-octyl-bromide, and FC-77) were used to examine the effects of density and kinematic viscosity on volume recovered and maximum expiratory flow. It was demonstrated that flow limitation occurs during gravitational drainage when the airway pressure is < or = -15 cm H(2)O, and that this critical value of pressure did not depend on mouth pressure or perfluorocarbon type. The perfluorocarbon properties affect the volume recovered, maximum expiratory flow, and the time to drain, with the most viscous perfluorocarbon (perfluorodecalin) taking the longest time to drain and resulting in lowest maximum expiratory flow. Perfluoro-octyl-bromide resulted in the highest recovered volume. The findings of this study are relevant to the selection of perfluorocarbons to reduce the occurrence of flow limitation and provide adequate minute ventilation during total liquid ventilation.

Animals↗
PubMed1999

Nematic ordering of rigid rods in a gravitational field.

The isotropic-to-nematic transition in an athermal solution of long rigid rods subject to a gravitational (or centrifugal) field is theoretically considered in the Onsager approximation. The new feature emerging in the presence of gravity is a concentration gradient that coupled with the nematic ordering. For rodlike molecules this effect becomes noticeable at centrifugal acceleration g approximately 10(3)-10(4) m/s(2), while for biological rodlike objects, such as tobacco mosaic virus, the effect is important even for normal gravitational acceleration conditions. Rods are concentrated near the bottom of the vessel, which sometimes leads to gravity induced nematic ordering. The concentration range corresponding to phase separation increases with increasing g. In the region of phase separation the local rod concentration, as well as the order parameter, follow a step function with height.

Journal Article↗
PubMed2000

Thermodynamics of self-gravitating systems with softened potentials

The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in a mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is achieved by truncating to N terms an expansion of the Newtonian potential in spherical Bessel functions. The order N is related to the softening at short distances. This regularization has the remarkable property that it allows for an exact solution of the mean-field equation. It is found that for N not too large the absolute maximum of the entropy coincides to high accuracy with the solution of the Lane-Emden equation, which determines the mean-field mass distribution for the Newtonian potential for energies larger than E(c) approximately -0.335GM(2)/R. Below this energy a collapsing phase transition, with negative specific heat, takes place. The dependence of this result on the regularizing parameter N is discussed.

Journal Article↗
PubMed2000

Gravitational phase transitions in a one-dimensional spherical system

The behavior of gravitational phase transitions in a system of concentric, spherical, mass shells that interact via their mutual and self gravitation is investigated. The nature of the transition in the microcanonical, canonical, and grand canonical ensembles is studied both theoretically in terms of the mean field limit and by dynamical simulation. Transitions between a quasiuniform state and a centrally concentrated state are predicted by mean field theory for the microcanonical and canonical ensembles, and this is supported by dynamical simulation. For the grand canonical ensemble, mean field theory predicts that no transition takes place, and that the thermodynamically stable state is always the uniform one. Again, this is supported by simulations under various initial distributions of mass, even when the system is initialized in a collapsed state. In addition to testing the predictions of the mean field theory and studying the effects of finite size scaling, dynamical simulation allowed us to examine the behavior of temporal and positional correlations which are predicted to vanish in the mean field limit.

Journal Article↗
PubMed2000

Mean field theory of spherical gravitating systems

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems confined in a finite domain consisting of either point masses or rotating mass shells of different dimension. We establish a direct connection between the spherically symmetric equilibrium states of a self-gravitating point mass system and a shell model of dimension 3. We construct the equilibrium density functions by maximizing the entropy subject to the usual constraints of normalization and energy, but we also take into account the constraint on the sum of the squares of the individual angular momenta, which is also an integral of motion for these symmetric systems. Two statistical ensembles are introduced that incorporate the additional constraint. They are used to investigate the possible occurrence of a phase transition as the defining parameters for each ensemble are altered.

Journal Article↗
PubMed2001

Localized electromagnetic and weak gravitational fields in the source-free space.

Localized electromagnetic and weak gravitational time-harmonic fields in the source-free space are treated using expansions in plane waves. The presented solutions describe fields having a very small (about several wavelengths) and clearly defined core region with maximum intensity of field oscillations. In a given Lorentz frame L, a set of the obtained exact time-harmonic solutions of the free-space homogeneous Maxwell equations consists of three subsets (storms, whirls, and tornados), for which time average energy flux is identically zero at all points, azimuthal and spiral, respectively. In any other Lorentz frame L', they will be observed as a kind of electromagnetic missile moving without dispersing at speed V<c. The solutions that describe finite-energy evolving electromagnetic storms, whirls, tornados, and weak gravitational fields with similar properties are also presented. The properties of these fields are illustrated in graphic form.

Journal Article↗
PubMed2002

Statistical mechanics of relativistic one-dimensional self-gravitating systems.

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of N particles coupled to lineal gravity and can be considered as a model of N relativistically interacting sheets of uniform mass. The partition function and one-particle distribution functions are computed to leading order in 1/c where c is the speed of light; as c --> infinity results for the nonrelativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its nonrelativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the nonrelativistic case.

Journal Article↗
PubMed2002

Angular-momentum-induced phase transition in spherical gravitational systems: N-body simulations.

The role of thermodynamics in the evolution of systems evolving under purely gravitational forces is not completely established. Both the infinite range and singularity in the Newtonian force law preclude the use of standard techniques. However, astronomical observations of globular clusters suggest that they may exist in distinct thermodynamic phases. Here, using dynamical simulation, we investigate a model gravitational system that exhibits a phase transition in the mean-field limit. The system consists of rotating, concentric, mass shells of fixed angular-momentum magnitude and shares identical equilibrium properties with a three-dimensional point mass system satisfying the same condition. The mean-field results show that a global entropy maximum exists for the model, and a first order phase transition takes place between "quasi-uniform" and "core-halo" states, in both the microcanonical and canonical ensembles. Here we investigate the evolution and, with time averaging, the equilibrium properties of the isolated system. Simulations were carried out in the transition region, at the critical point, and in each clearly defined thermodynamic phase, and striking differences were found in each case. We find full agreement with mean-field theory when finite-size scaling is accounted for. In addition, we find that (1) equilibration obeys power-law behavior, (2) virialization, equilibration, and the decay of correlations in both position and time, are very slow in the transition region, suggesting that the system is also spending time in the metastable phase, and (3) there is a strong evidence of long-lived, collective oscillations in the supercritical region.

Journal Article↗
PubMed2002

Statistical mechanics of the self-gravitating gas with two or more kinds of particles.

We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble, which we express as a functional integral over the densities of the two kinds of particles for a large number of particles. The system is shown to possess an infinite volume limit when (N(1),N(2),V)--> infinity, keeping N(1)/V(1/3) and N(2)/V(1/3) fixed. The saddle point approximation becomes here exact for (N1,N2,V)--> infinity. It provides a nonlinear differential equation for the densities of each kind of particle. For the spherically symmetric case, we compute the densities as functions of two dimensionless physical parameters: eta(1)=Gm(2)(1)N(1)/V(1/3)T and eta(2)=Gm(2)(2)N(2)/V(1/3)T (where G is Newton's constant, m(1) and m(2) the masses of the two kinds of particles, and T the temperature). According to the values of eta(1) and eta(2) the system can be either in a gaseous phase or in a highly condensed phase. The gaseous phase is stable for eta(1) and eta(2) between the origin and their collapse values. We have thus generalized the well-known isothermal sphere for two kinds of particles. The gas is inhomogeneous and the mass M(R) inside a sphere of radius R scales with R as M(R) proportional to R(d) suggesting a fractal structure. The value of d depends in general on eta(1) and eta(2) except on the critical line for the canonical ensemble in the (eta(1),eta(2)) plane where it takes the universal value d approximately 1.6 for all values of N(1)/N(2). The equation of state is computed. It is found to be locally a perfect gas equation of state. The thermodynamic functions (free energy, energy, entropy) are expressed and plotted as functions of eta(1) and eta(2). They exhibit a square root Riemann sheet with the branch points on the critical canonical line. The behavior of the energy and the specific heat at the critical line is computed. This treatment is further generalized to the self-gravitating gas with n types of particles.

Journal Article↗
PubMed2002

Low-frequency electrostatic waves in self-gravitating dusty plasmas with dust-ion collisions.

The influence of dust-ion collisions on low-frequency modes in a self-gravitating dusty plasma is studied. The stability of the system is easily determined using elementary principles of rootlocus theory. It shows that collisions between ions and dust grains do not change the criteria for gravitational collapse at any value of their collision frequency, but diminish the growth rate of unstable dusty plasmas. Moreover, the rootlocus plots visualize qualitatively the evolution of the real frequencies and damping decrements of the dust-acoustic and ion-acoustic modes as the dust-ion collision frequency increases.

Journal Article↗
PubMed2002

Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions.

We address the thermodynamics and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. We study the equilibrium density profile and phase diagram of isothermal spheres and, for 2<D<10, determine the onset of instability in the series of equilibria. We also study the dynamics of self-gravitating Brownian particles in a high friction limit leading to the Smoluchowski-Poisson system. Self-similar solutions describing the collapse are investigated analytically and numerically. In the canonical ensemble (fixed temperature), we derive the analytic form of the density scaling profile which decays as f(x) approximately x(-alpha), with alpha=2. In the microcanonical ensemble (fixed energy), we show that f decays as f(x) approximately x(-alpha(max)), where alpha(max) is a nontrivial exponent. We derive exact expansions for alpha(max) and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features with, in particular, the formation of a Dirac peak in the density profile.

Journal Article↗