Static solutions of the Brans-Dicke equations

It is shown that, given any static solution of the Einstein vacuum equations, a corresponding family of static vacuum solutions of the Brans-Dicke equations can be written down by inspection. Spherically and axially symmetric fields are considered explicitly. It is demonstrated how some solutions of the Brans-Dicke equations may be obtained without having to solve any field equations explicitly at all.     

Exact solutions of vacuum Brans-Dicke equations

Vacuum Stäckel type (2.1) spaces are classified in Brans-Dicke theory for the case when the scalar field depends on all the variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 86–90, January, 1992.     

Common solutions of the einstein and Brans-Dicke theories

It is shown that non-trivial solutions common to the vacuum field equations of the Einstein and of the Brans-Dicke theories necessarily representpp-waves and the set of all common solutions is precisely the set of allpp-wave solutions of the Einstein equations. The form of the associated scalar field is found and is shown to be singular when ω相似文献   

Solving Bertolami's equations for Brans-Dicke cosmological models

Solutions are developed for Berman and Som's formulation of Bertolami's equations for a Brans-Dicke cosmology with time-dependent cosmological term. Physical constraints are applied to these solutions to deduce conditions necessary for constructing plausible cosmological models in this theory.     

Homothetic self-similar solutions of three-dimensional Brans-Dicke gravity

All homothetic self-similar solutions of the Brans-Dicke scalar field in three-dimensional spacetime with circular symmetry are found in closed form.     

Bianchi type-I solutions for modified Brans-Dicke cosmology

Cosmological dust solutions have been obtained in Bianchi type-I homogeneous space for Brans-Dicke modified theory by the condition of the cosmological parameter ().     

Exact solutions in Brans-Dicke theory with bulk viscosity

The effect of bulk viscosity on the evolution of the homogeneous and isotropic cosmological models in the Brans-Dicke theory of gravitation is studied. Solutions are found, with a baratropic equation of state, a time-independent bulk viscosity, the gravitational constant inversely proportional to the age of the universe, and the mass of the universe (in the closed model) proportional to the square of its age; the expansion factor is a linear function of the cosmological time. For flat space, power law expansions are found, among them one that is related to extended inflation.     

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.     

General solutions for a cosmological Robertsonwalker metric in the Brans-Dicke theory

The general vacuum solutions of the Brans-Dicke theory in a cosmological Robertson-Walker-type metric are explicitly given. Several families of solutions have properties which essentially differ from the conventional Einstein theory. The geometry is not uniquely determined by the equations of motion, raising doubts about the “Machian” character of the Brans-Dicke theory. The role of the cosmological constant is emphasized, in agreement with modern ideas of fundamental particle interactions.     

General solutions for a static isotropic metric in the Brans-Dicke gravitational theory

The complete set of vacuum solutions for the metric tensor of a static spherically symmetric field is given, some of these solutions showing the remarkable feature of not agreeing-even in first order-with the classically well-known weak-field solutions of the Brans-Dicke (B.D.) equations. The existence of a particular two-parameter family of solutions raises severe doubts about the so-called Machian aspect of B.D. theory.     

Isotropic solutions of the Einstein-Boltzmann equations

We prove that theP()₂ quantum field theory satisfies the spectral condition. The space time translationa=(x, t) is implemented by the unitary groupU(a)=exp(itH–ixP), and the joint spectrum of the energy operatorH and the momentum operatorP is contained in the forward cone. We also obtain bounds on certain vacuum expectation values of products of field operators. Our proofs involve an analysis of the limitV for approximate theories in a periodic box of volumeV. Assuming the existence of a uniform mass gap, we are able to establish all the Wightman axioms with the exception of the Lorentz invariance of the vacuum.Supported in part by the Air Force Office of Scientific Research, Contract AF 49(638)-1719.Alfred P. Sloan Foundation Fellow. Supported in part by the Air Force Office of Scientific Research, Contract F 44620-70-C-0030.     

Null solutions of the Yang-Mills equations

We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays.Alexander von Humboldt Fellow. Address after 31 May 1986: Institute of Theoretical Physics, University of Warsaw, Hoa 69, 00-681 Warsaw, Poland.     

Iterative solutions of the Lotka-Volterra equations

Summary Lotka-Volterra equations for two-species predator-prey system are solved by an iteration method. The first iteration step reproduces elliptical trajectories known from the linearization treatment. The second iteration step leads to analytical expressions describing large-amplitude motions and lying beyong the elliptical approximation. The range of validity of the method is discussed. It is shown that deviations from the exact trajectories increase if the initial state is far from the centre of motion. For illustration some trajectories are calculated showing a good agreement with trajectories obtained by numerical methods.     

Pseudoparticle solutions of the Yang-Mills equations

We find regular solutions of the four dimensional euclidean Yang-Mills equations. The solutions minimize locally the action integrals which is finite in this case. The topological nature of the solutions is discussed.     

Exact solutions of the Altarelli-Parisi equations

Evolution equations for single species parton distributions are solved analytically. For infrared-convergent theories the solutions can be expressed in a closed form as convolutions over Bessel functions. For infrared-divergent theories, such as QCD, the exact solution involves an infinite number of convolutions. The accuracy of various approximations to this solution is estimated.