Stationary axisymmetric solutions of the Jordan-Brans-Dicke equations with electromagnetic sources

Any stationary axisymmetric solution of the coupled JBD-Maxwell field equations such thatF _ab ^* t^ab vanishes, can be determined from a composition of any stationary axisymmetric Einstein-Maxwell spacetime with the Weyl class of metrics.     

Stationary axisymmetric perfect fluid solutions in general relativity

A new class of exact solutions of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. The class of solutions is invariantly characterized by means of the following properties: (i) The energy-momentum tensor describes a perfect fluid. (ii) There are two commuting Killing vectors and which form an abelian groupG ₂ of motion. (iii) There is a timelike Killing vector parallel to the four-velocity of the fluid (rigid rotation of the fluid). (iv) The four-vector of the angular velocity of the fluid is a gradient ⁱ=–(1/4_c)^irklU_l (U_r:k–U_k:r)= ⁱ. The last assumption is the reason that all solutions of this class can be found by solving an ordinary differential equation of the second order.     

Stationary and static axisymmetric perfect fluid solutions

Using a certain formalism for the stationary axisymmetric problem with source a rigidly rotating perfect fluid it is shown that under specific assumptions, covariantly imposed, the field equations are reduced to a system of two ordinary second order differential equations. Two known metrics are special solutions of this system. In addition two static axisymmetric perfect fluid solutions, with a spherically symmetric limit, are derived explicitly.     

Stationary axisymmetric solutions of three-dimensional Einstein gravity

Einstein theory in three space-time dimensions is studied in the stationary, rotationally symmetric regime. Explicit interior solutions for various types of matter sources are found and their properties discussed.     

Stationary axisymmetric fields in a teleparallel theory of gravitation

The existence of a set of tetrads satisfying the Møller equations and leading to the Kerr metric is proved by using a particular procedure, which could be very useful to deal with other stationary axisymmetric cases of general relativity in the framework of Møller's theory of gravitation.     

Brane world cosmology in Jordan-Brans-Dicke theory

We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.     

Some astrophysical consequences of the Jordan-Brans-Dicke theory

It is shown that the appearance of a new dimensional constant — the speed of light — in the field equations of the Jordan-Brans-Dicke theory (JBD) makes it possible to construct from the set of constant constructions appearing in the system two with the dimension of energy. This is an indication of the existence of two branches of equilibrium configurations in the JBD theory, which was discovered from numerical calculations by Saakyan and Mnatsakanyan. The problem of the gravitational stability of the cosmological model of the JBD theory is considered. It is shown that the two modes of perturbation evolution obtained differ little from the perturbation modes in the Friedmann model.This article is the result of work performed under the direction of Candidate of Physical and Mathematical Sciences V. I. Bashkov.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 24–27, February, 1982.     

关于稳态轴对称真空引力场方程的两个扩展解

将Ehlers变换应用于Ernst方程的Schwarzschild解和Kerr解，通过引入Boyer-Lindquist坐 标变换以及相关的参数代换，得到了Ernst方程的两个扩展解. 当所含参数L=0时，其中一个扩展解退化为Schwarzschild解，另一个退化为Kerr解.当参数|L|M时，如果取近似1-LM2≈1，则这两个扩展解分别退化为已知的NUT-Taub解和Kerr-NUT解.这一结果表明 NUT-Taub解和Kerr-NUT解中所含的参数l并非能任意取值，它的取值要受到引力源质量M的限 制，即要求|l|M. 关键词： Ehlers变换群 Ernst方程 Boyer-Lindquist坐标变换     

A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

Stationary axially symmetric electrovac solutions in the general scalar-tensor theory

A method is presented which reduces the Bergmann-Wagoner-Nordtvedt field equations for a stationary axisymmetric electrovac space-time, to the Einstein-Maxwell equations. In this formalism the solution generation technique of Singh and Rai for Brans-Dicke theory yields a particular class of solutions, for which the conformal scalar field depends upon the radial coordinate only. As an application of the method, new cylindrically symmetric and nonstatic scalar-Maxwell solutions are obtained for null and non-null electromagnetic fields.     

Generalizations of the Kerr-Newman and charged Tomimatsu-Sato metrics in the Jordan-Brans-Dicke theory

A procedure to construct stationary axisymmetric solutions of the Jordan-Brans-Dicke field equations with electromagnetic sources is obtained solutions, since they are compositions of Weyl static solutions with the given stationary ones, are equipped with several parameters, as many as one wishes.     

Stationary axisymmetric solutions of the Einstein equations with rigidly rotating perfect fluid and nonlinear charged sources

A class of stationary, rigidly rotating perfect fluids coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found for the equation of state 3p+=const. We use a structure function for the Born-Infeld nonlinear electrodynamics which is invariant under duality rotations and a metric possessing a four-parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.     

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.     

Stationary vacuum fields with a conformally flat three-space I. General theory

A generalized notion of conformastat space-times is introduced in relativity theory. In this sense, the conformastat space-time is stationary with the three-space of timelike Killing trajectories being conformally flat. A 3+1 decomposition of the field equations is given, and two classes of nonstatic conformastat vacuum fields are exhaustively investigated. The resulting three metrics form a NUT-type extension of the solution of the static conformastat vacuum problem. We conjecture that all conformastat vacuum space-times are axially symmetric.     

Neutron stars and incompressible fluid spheres in the Jordan-Brans-Dicke theory of gravitation

Neutron stars and incompressible fluid spheres are considered in the Jordan-Brans-Dicke theory. It is shown that their parameters (mass, radius, surface redshift) do not differ appreciably from the corresponding Einstein values even for ω = 0and various semi-realistic equations of state. For incompressible fluid spheres the differences between both theories of gravitation are most pronounced. We find an apparent instability of the incompressible fluid.     

Stationary axisymmetric space-times: A new approach

This essay describes a new approach to the problem of understanding stationary axisymmetric solutions of Einstein's vacuum equations, different from the “Bäcklund transformation” approach which has recently been extensively developed. It translates the problem into one of complex geometry, using the machinery of twistor theory. This, in turn, leads to a procedure which, in principle, generates all solutions. Some explicit examples are presented.     

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

In this paper we investigate spherically symmetric vacuum solutions of f(R) gravity in a higher-dimensional spacetime. With this objective we construct a system of non-linear differential equations whose solutions depend on the explicit form assumed for the function F(R)=\fracdf(R)dRF(R)=\frac{df(R)}{dR} . We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting F(R) close to the unity.