Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaître–Tolman–Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.     

The generalized second law in universes with quantum corrected entropy relations

We apply the generalized second law of thermodynamics to discriminate among quantum corrections (whether logarithmic or power-law) to the entropy of the apparent horizon in spatially Friedmann–Robertson–Walker universes. We use the corresponding modified Friedmann equations along with either Clausius relation or the principle of equipartition of the energy to set limits on the value of a characteristic parameter entering the said corrections.     

Extremum complexity distribution of a monodimensional ideal gas out of equilibrium

The extremum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is analytically approximated. In a first approximation, it consists of a double non-overlapping Gaussian distribution. In good agreement with this result, the numerical simulations of a particular isolated monodimensional gas, which is abruptly pushed far from equilibrium, shows the extremum complexity distribution in the decay of the system toward equilibrium.     

Letter: Self-Similar Bianchi Type VIII and IX Models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admits a four dimensional group of homotheties is given.     

Integrable multicomponent perfect fluid multidimensional cosmology. I

Multidimensional cosmological models with a space-time consisting ofn (n 2) Einstein spaces are investigated for a special class of multicomponent perfect fluid as a matter source. The dynamical behaviour of the universe is described. In the case of static internal spaces the external space evolves like a Friedmann universe with changing effective equation of state. Some of the models considered are integrable and classical as well as quantum solutions are found. Some of them represent wormholes. Quantum wormholes have a discrete spectrum.     

On the stochasticity in relativistic cosmology

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.     

No periodic orbits for the type A Bianchi's systems

It is known that the 6 models of Bianchi class A have no periodic solutions. In this article we provide a new, direct, unified and easier proof of this result.     

An inhomogeneous model universe behaving homogeneously

We present a new model universe based on the junction of FRW to flat Lemaitre–Tolman–Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distance relation as for the CDM/FRW models, a negative deceleration parameter near the observer, and correct linear and non-linear density contrast. As a whole, the model behaves like a FRW model on the past light cone with a special behavior of the scale factor, Hubble and deceleration parameter, mimicking dark energy. Paper in honor of Bahram Mashhoon’s 60th birthday.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Local Scale Invariance and General Relativity

According to the theory of unimodular relativity developed by Anderson and Finkelstein, the equations of general relativity with a cosmological constant are composed of two independent equations, one which determines the null-cone structure of space-time, another which determines the measure structure of space-time. The field equations that follow from the restricted variational principle of this version of general relativity only determine the null-cone structure and are globally scale-invariant and scale-free. We show that the electromagnetic field may be viewed as a compensating gauge field that guarantees local scale invariance of these field equations. In this way, Weyl's geometry is revived. However, the two principle objections to Weyl's theory do not apply to the present formulation: the Lagrangian remains first order in the curvature scalar and the nonintegrability of length only applies to the null-cone structure.     

Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium

Density distribution of an ideal Maxwellian gas confined in a finite domain is not uniform even in thermodynamic equilibrium. Near to the boundaries, there is a layer in which the density goes to zero. Existence of this boundary layer explains the shape and size dependence of the thermodynamic quantities in nano scale.     

Steady-state electric discharge in a weakly ionized gas at thermal equilibrium

The similarity properties of a discharge in a weakly ionized gas at thermal equilibrium are examined. The conditions for a developed discharge are shown to be governed by a dimensionless discharge parameter. An explicit dependence of the discharge parameter on the potential difference, the pressure, and the type of gas is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 2, No. 4, pp. 116–120, April, 1969.     

Inhomogeneous cosmological models with heat flux

We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.     

Thermodynamical equilibrium and spacetime geometry

In relativistic theory of irreversible thermodynamical processes near equilibrium, generally a series of assumptions is made having, in particular, the consequence that the temperature vector is a Killing vector. We show that, in contrast to usual approaches, in equilibrium (i) the temperature vector can also be a conformal Killing vector, (ii) as an implication of the Killing property of the temperature vector, most assumptions made can be derived, without restricting the matter configuration to a perfect fluid, (iii) for non-vanishing rotation of the fluid, the heat-flow is unequal to zero, (iv) for vanishing acceleration of the fluid the Friedmann radiation cosmos is the only physically significant solution of Einstein's equations and (v) the equilibrium conditions are of the Cattaneo form such that a causal propagation of temperature can be expected.     

Controlling a complex dynamical network to attain an inhomogeneous equilibrium

Many networks are made up of a few groups, with nodes in the same group having the same kind of function. In this work, the problem of controlling a complex dynamical network to attain an inhomogeneous equilibrium point is investigated, which means that nodes in the same group achieve the same equilibrium point as an isolated node, while different groups correspond to different equilibrium points. An open-loop constant control approach is first proposed to obtain the inhomogeneous equilibrium point of the network. Then, the feedback pinning control approach is applied to make the inhomogeneous equilibrium point asymptotically stable.     

Tachyonic Dark Matter

Recent attempts to explain the dark matter and energy content of the universe have involved some radical extensions of standard physics, including quintessence, phantom energy, additional space dimensions, and variations in the speed of light. In this paper I consider the possibility that some dark matter might be in the form of tachyons. I show that, subject to some reasonable assumptions, a tachyonic cosmological fluid would produce distinctive effects, such as a surge in quantum vacuum energy and particle creation, and a change in the conventional temperature–time relation for the normal cosmological material. Possible observational consequences are discussed.     

Thermodynamic theory of equilibrium fluctuations

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.     

Letter: A Study of Asymptotic Behavior of Homogeneous Cosmological Models with a Varying Cosmological Constant in Einstein-Cartan Theory: Cosmic No-Hair Theorem

We have investigated cosmic no-hair theorem with varying cosmological constant in homogeneous anisotropic Bianchi-models for Einstein-Cartan theory. We have taken the variation of to be as the square of the extrinsic curvature scalar and asymptotic behavior has been studied.