Singularity-free Solutions Research Articles

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

We show that global asymptotically flat singularity-free solutions of the spherically symmetric Vlasov-Einstein system exist for all initial data which are sufficiently small in an appropriate sense. At the same time detailed information is obtained concerning the asymptotic behaviour of these solutions. A key element of the proof which is also of intrinsic interest is a local existence theorem with a continuation criterion which says that a solution cannot cease to exist as long as the maximum momentum in the support of the distribution function remains bounded. These results are contrasted with known theorems on spherically symmetric dust solutions.

Asymptotic freedom from induced gravity cosmology

We give conditions to obtain cosmological asymptotic freedom in scalar-tensor theories of gravity. We show that this feature can be achieved in FRW flat spacetimes since we obtain singularity free solutions where the effective gravitational constant G eff → 0 for t → −∞ and, for some of them, G eff → G N for t → ∞, where G N is the Newton constant.

Singularity-free cylindrically symmetric solutions in Kaluza-Klein space-time.

Five-dimensional singularity-free solutions are obtained for free space as well as a stiff fluid. They may be said to be the generalizations in Kaluza-Klein space-time of the recently discovered four-dimensional cylindrically symmetric solutions, which are free from the initial big bang singularity. Our higher dimensional metrics have the interesting property that in the course of time some of them show dimensional reduction, so that at the late stages of evolution we get effectively the familiar four-dimensional space-time.

Fundamental constants in singularity-free five-dimensional Kaluza-Klein cosmological model

Expressions for the time dependence of the fundamental constants are derived through dimensional reduction and one-loop quantum corrections to scalar fields. Moreover, singularity-free solutions of Einstein's field equations are obtained. Using these solutions, we discuss the time dependence of fundamental constants. It is interesting to see that the fine structure constant asymptotically approaches to 1/137,G eff (effective four-dimensional constant) approachesG N (Newtonian gravitational constant), and λeff vanishes. Graphical representations of these results are also given for a special case.

Static solutions of the spherically symmetric Vlasov–Einstein system

AbstractWe consider the Vlasov—Einstein system in a spherically symmetric setting and prove the existence of static solutions which are asymptotically flat and have finite total mass and finite extension of the matter. Among these there are smooth, singularity-free solutions, which have a regular centre and have isotropic or anisotropic pressure, and solutions which have a Schwarzschild-singularity at the centre.

On the existence of singularity-free solutions in quadratic gravity

We study a general field theory of a scalar field coupled to gravitation through a quadratic Gauss-Bonnet term ξ( φ) R GB 2. We show that, under mild assumptions about the function ξ(φ), the classical solutions in a spatially flat FRW background include singularity-free solutions.

Solution of dirac equation in a singularity-free Kaluza-Klein cosmological model

The singularity-free solution of (4 + D) -dimensional Einstein field equations for the Kaluza-Klein cosmological model is obtained. Then the Dirac equations are solved in this model.

A comment on the Brans-Dicke cosmology for a radiation universe

The cosmological solutions of Brans-Dicke theory for a radiation universe obtained so far are commented on. Some problematic solutions are corrected and the conditions corresponding to singularity-free solutions are investigated.

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

We show that global asymptotically flat singularity-free solutions of the spherically symmetric Vlasov-Einstein system exist for all initial data which are sufficiently small in an appropriate sense. At the same time detailed information is obtained concerning the asymptotic behaviour of these solutions. A key element of the proof which is also of intrinsic interest is a local existence theorem with a continuation criterion which says that a solution cannot cease to exist as long as the maximum momentum in the support of the distribution function remains bounded. These results are contrasted with known theorems on spherically symmetric dust solutions.

Cosmological solutions of theN=2,D=5 supergravity with the Gauss-Bonnet term

We study the cosmological solutions of theN=2,D=5 supergravity theory modified by the presence of the Gauss-Bonnet term. Our interest is focused on the singularity-free solutions, in both the internal and the external spaces. In fact, there is a family of solutions which possess the desired features.

General class of inhomogeneous perfect-fluid solutions.

We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.

Design of a viscous ring nutation damper for a freely precessing body

A ring damper partially filled with mercury for removing the wobble motion of a freely precessing body is analyzed. Coupled equations of motion of the rotor and mercury are derived in terms of Euler parameters and quasicoordinates for the purposes of computational efficiency and singularity-free solution when the nutation angle approaches zero. An experiment is made to verify the theoretical solution of the nutation angle obtained by numerical integration of the equations of motion. The best choice of parameters of the damper is obtained by solving a minimum-time optimization problem that minimizes the time elapsed in the nutation-synchronous mode as well as the residual nutation angle in the spin-synchronous mode. The results show that the decay of the nutation angle can be accelerated to a great extent if the damper is properly designed.

Features of some solutions of a gravitational theory with a scalar field

We study some solutions of a gravitational theory with a scalar field and find that in some cases a singularity free solution may be present.

A singularity-free cosmological model in ECSK theory

In the framework of the ECSK [Einstein-Cartan-Sciama-Kibble] theory of cosmology, a scalar field nonminimally coupled to the gravitational field is considered. For a Robertson-Walker open universe (k=0) in the radiation era, the field equations admit a singularity-free solution for the scale factor. In theory, the torsion is generated through nonminimal coupling of a scalar field to the gravitation field. The nonsingular nature of the cosmological model automatically solves the flatness problem. Further absence of event horizon and particle horizon explains the high degree of isotropy, especially of 2.7-K background radiation.

Exact interior solutions in Einstein–Cartan–Yukawa theory

A simple method of obtaining singularity-free interior solutions in Einstein–Cartan–Yukawa theory is presented here. The validity of the solution is shown by considering two types of configurations, one Schwarzschild-like and the other Tolman-IV-like. We recover the Schwarzschild and Tolman-IV solutions as soon as the Cartan and Yukawa effects are switched off. In both cases the necessary physical conditions are satisfied. The possible role of torsion in halting the collapse of a massive star is also studied.

Einstein: Distant parallelism and electromagnetism

Einstein's approach to unified field theories based on the geometry of distant parallelism is discussed. The simplest theory of this type, describing gravitation and electromagnetism, is investigated. It is found that there is a charge-current density vector associated with the geometry. However, in the static spherically symmetric case no singularity-free solutions for this vector exist.

Dynamic analysis of large-scale mechanical systems and animated graphics

This paper presents a computer-based method for formulation and solution of coupled differential and algebraic equations describing large-scale mechanical systems, including feedback control, aerodynamic forces, and other multidisciplinary effects that interact with the mechanical system. A Euler parameter repersentation of the configuration of the mechanical system is employed to obtain singularity free solution for generalized coordinates and a much simplified algebraic formulation of the governing system of equations, compared with the more classical Euler angle generalized coordinate formulation. A generalized coordinate partitioning algorithm is employed to identify independent generalized coordinates automatically and reduce the dimension of the numerical integration problem. Animated graphics output is employed to assist in visualization of dynamic performance of several systems—a parachute descending in air, an aircraft landing on a damaged runway, and a truck with flexible chassis.

An L2approach to the solution of coupled-channel scattering equations

It is proposed to solve a coupled-channel scattering equation representing the effect of all but a few channels by an optical potential. This optical potential is expanded on an L2 basis and it is shown how the resulting pseudoresonances can be eliminated using the 'equivalent weight' hypothesis of Heller (1973). These ideas are applied to a model problem posed by Burke, Berrington and Sukumar (1981) and accurate singularity-free solutions are obtained. The extension of the method to electron-atom scattering is discussed.

Gravitation without black holes

In recent years much work has been devoted to the development of the (i singularity theorems ~ of Hawking and Penrose in order to have a bet ter understanding of the properties of space-times in Einstein 's general theory of re la t iv i ty (1). In spite, however, of the significant advances made in the subject, many impor tant problems of the classical theory of singularities remain still unsolved. The results obtained t i l l now, support the feeling tha t physically realistic solutions to the Einstein 's equations that are singulari ty free can only be obtained either by modifying the field equations or by looking for some missing physics in the applied general relat ivi ty. To be more concrete, let us consider the singulari ty which occurs in deriving the metric external to a static spherically symmetr ic body of mass qn, tha t is the Schwarzschild curvature singularity. This is a part icularly simple situation so, assuming the val id i ty of Einstein 's equations of general relativity, we can t ry to look for a minimal physical ansatz which can lead to singularity-free solutions. The most obvious suggestion might be to explore which physical proper ty one could at t r ibute to the body, besides its mass m, in order to get a well-behaved line element. Otherwise stated, between the many parameter familes of asymptot ical ly flat solutions which generalize che Schwarzschild case, one should succeed in choosing a suitable set of parameter to which correspond regular solutions. In stat ionary nonspherieal situations, however, i t is known tha t the Kerr-Newman solutions, where the parameters are the mass m, the electric charge q, the magneticmonopole charge p and a rotation parameter a, still display horizons, naked singularities and other unwanted phenomena. The simplest generalization of the Schwarzsehild problem, in which to the mass m is associated a scalar charge a, does not seem to have been adequately t reated in the li terature.

Conformally flat charged dust

It is proved that the most general conformally flat singularity-free solution for charged dust in static equilibrium must be spherically symmetric and the solution is unique. It matches with exterior Reissner-Nordstrom metric. The manifest form of the metric conformal to Minkowskian metric is also given.