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.     

Brane Cosmology From Heterotic String Theory

We consider brane cosmologies within the context of five-dimensional effective actions with higher curvature corrections. The actions are compatible with bulk string amplitude calculations from heterotic string theory. We find wrapped solutions that satisfy the field equations in an approximate but acceptable manner given their complexity, where the internal, four-dimensional, scale factor is naturally inflating, having an exponential De-Sitter form. The temporal dependence of the metric components is nontrivial so that this metric cannot be factored as in a conformally flat case. The effective Planck mass is finite and the brane solutions can localize four-dimensional gravity while the four-dimensional gravitational constant varies with time. The Hubble constant can be freely specified through the initial value of the scalar field, to conform with recent data.     

Axisymmetric stationary solutions as harmonic maps

We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commuting Killing vectors. This method consists of writing the axisymmetric stationary Einstein equations in vacuum as a harmonic map which belongs to the groupSL(2,), and decomposing it into its harmonic submaps. This method provides a natural classification of the solutions in classes (Weyl's class, Lewis' class etc.).On leave of absence from Warsaw University, Warsaw, Poland     

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.     

A new class of stationary solutions to the five-dimensional Kaluza-Klein field equations

Using the five-dimensional potential formalism, a set of six new stationary axisymmetric solutions to the Kaluza-Klein field equations are constructed from the one dimensional subspace of the potential space. All the solutions have scalar potential and magnetic field, two of them possess magnetic monopoles and the other describes a magnetic dipole.     

Stationary axisymmetric solutions in the vacuum Jordan-Brans-Dicke theory

It is shown that any stationary axisymmetric solution to the vacuum field equations of the Jordan-Brans-Dicke (JBD) theory may be obtained from a composition of any stationary axisymmetric vacuum Einstein spacetime with the Weyl class of metrics. Thus, generating solution techniques can be used to obtain any stationary axisymmetric JBD vacuum solution. In this manner, C. B. G. McIntosh's results concerning this topic are improved upon.     

A new class of asymptotically flat stationary axisymmetric vacuum gravitational fields

We present the full four-dimensional metric for a stationary axisymmetric solution of the vacuum Einstein equations related to the Ernst potential which we obtain by application of anarbitrary number of rank-zero HKX transformations to the general static Weyl solution. The metric function is determined in a completely algebraically way. We perform a suitable Ehlers transformation to ensure asymptotic flatness and give the expression for the total mass of this asymptotically flat solution by analyzing the behavior of the solution on the positive z axis.     

The matter-vacuum matching problem in general relativity

In a recent paper [1] methods were developed for studying the problem of matching matter and vacuum solutions of Einstein's field equations along timelike hypersurfaces in the axisymmetric stationary case. Criteria for the existence and uniqeness of perfect fluid sources for given vacuum fields were given in the form of a theorem. As an application, the existence of such Kerr-interior solutions could be proved at least in a full neighborhood of suitably chosen boundary surfaces.In this paper further investigations of this matching problem are made for some special cases. It is found that stationary rotating dust cannot be a source of the Kerr metric and the existence of rotating Schwarzschild sources is proved. These results are discussed together with further aspects of the general methods used.Work supported by the Deutsche Forschungsgemeinschaft.     

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einstein's four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.     

Imitation of matter by a scalar field in five-dimensional Kaluza-Klein theory

The interpretation of the scalar field ={ie96-1} in the five-dimensional variant of Kaluza-Klein theory is considered. It is proposed that the scalar field be considered as the generalized potential of four material velocities. It can be shown that with additional limitations on the scalar field the right side of the split five-dimensional Einstein equations transform to a hydrodynamic energy-momentum tensor for an ideal liquid with a limited set of equations of state. Concrete five-dimensional metrics, which are obligatorily nonstationary, are analyzed from this viewpoint.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 111–117, January, 1995.     

Stars in five-dimensional Kaluza–Klein gravity

In the five-dimensional Kaluza–Klein (KK) theory there is a well known class of static and electromagnetic-free KK-equations characterized by a naked singularity behavior, namely the Generalized Schwarzschild solution (GSS). We present here a set of interior solutions of five-dimensional KK-equations. These equations have been numerically integrated to match the GSS in the vacuum. The solutions are candidates to describe the possible interior perfect fluid source of the exterior GSS metric and thus they can be models for stars for static, neutral astrophysical objects in the ordinary (four-dimensional) spacetime.     

A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.     

An investigation of embeddings for spherically symmetric spacetimes into Einstein manifolds

Embeddings into higher dimensions are very important in the study of higher-dimensional theories of our Universe and in high-energy physics. Theorems which have been developed recently guarantee the existence of embeddings of pseudo-Riemannian manifolds into Einstein spaces and more general pseudo-Riemannian spaces. These results provide a technique that can be used to determine solutions for such embeddings. Here we consider local isometric embeddings of four-dimensional spherically symmetric spacetimes into five-dimensional Einstein manifolds. Difficulties in solving the five-dimensional equations for given four-dimensional spaces motivate us to investigate embedded spaces that admit bulks of a specific type. We show that the general Schwarzschild–de Sitter spacetime and Einstein Universe are the only spherically symmetric spacetimes that can be embedded into an Einstein space of a particular form, and we discuss their five-dimensional solutions.     

The “complex trick” in five-dimensional relativity

The generation method developed by Newman et al. which creates from spherically symmetric solutions of the field equations by a complex coordinate transformation axisymmetric solutions is extended to five-dimensional relativity.     

Transcendent self-dual solutions for SU(2) gauge fields on euclidean four-dimensional space

By applying the method of separation of variables, we find a particular class of solutions of Yang's equations in the R-gauge for self-dual SU(2) static, axisymmetric gauge fields on euclidean four-dimensional flat space. The solutions obtained are depending functionally on a particular form of the fifth Painlevé transcendent.     

Axially symmetric stationary solutions of Einstein-Maxwell equations

A scheme is presented by which we can obtain static electrovac exterior solutions from the stationary gravitational fields given by Kerr and Tomimatsu and Sato. A five-parameter solution of the combined Einstein-Maxwell equations is given that describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds and angular momentum. These are generated by using Kinnersley's method from Wang's electrovac solutions, which, in turn, were generated from the gravitational fields of Tomimatsu and Sato for =2–3. All the solutions are asymptotically flat.     

Solutions of Einstein's field equations related to Jacobi's inversion problem

A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three-dimensional Laplace equation is presented. The solutions are related to Jacobi's inversion problem for hyperelliptic Abelian integrals.     

Scale invariance,killing vectors,and the size of the fifth dimension

An analysis is made of the classical five-dimensional sourceless Kaluza-Klein equations with the existence of the usual/ Killing vector not assumed, where is the coordinate of the fifth dimension. The physical distance around the fifth dimensionD ₅, needed for the calculation of the fine structure constant, is not calculable in the usual theory because the equations have a global scale invariance. In the present case, the Killing vector and the global scale invariance are not present, but it is found rather generally thatD ₅=0. This indicates that quantum gravity is a necessary ingredient if is to be calculated. It also provides an alternate explanation of why the universe appears four-dimensional.