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.     

Universal properties of distorted Kerr–Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein–Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr–Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.     

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.     

Stationary axisymmetric test fields on a Kerr metric

We determine explicitly the stationary axisymmetric Green's function of Teukolsky's equation.     

A new transcendent solution of Einstein's equations

One new stationary axisymmetric solution of the vacuum Einstein equations is obtained. It depends on a particular form of the fifth Painlevé transcendent.     

New exact solutions of Einstein's field equations: Gravitational force can also be repulsive!

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given.     

The uniqueness of the Schwarzschild interior metric

It is shown that every conformally flat axisymmetric stationary space-time is necessarily static, and that if the source is a perfect fluid then the space-time metric is the usual Schwarzschild interior metric.     

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 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.     

Comments on a paper by Collinson

The demonstration of the uniqueness of the Schwarzschild interior metric within conformally flat axisymmetric stationary spacetimes is revised. A complete proof containing the three possible branches of interior fluid solutions is given.     

Linear double universal Grassmann manifold method for the stationary axisymmetric vacuum gravitational field equations

Nagatomo's universal Grassmann manifold scheme is extended to a double form, which is used to find the exact solutions of the stationary axisymmetric vacuum gravitational field equations. Some new results are given.     

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is “rotating”—i.e., is such that the stationary Killing field is not everywhere normal to the horizon—must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, P. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.     

A relativistically rotating fluid cylinder

The field equations for stationary, axisymmetric, nonconvective perfect fluid are presented. A solution corresponding to a rigidly rotating cylinder with constant pressure is derived. Some properties of this solution are discussed.     

On the absence of scalar hair for charged rotating black holes in non-minimally coupled theories

In this work we check the validity of the no scalar hair theorem in charged axisymmetric stationary black holes for a wide class of scalar tensor theories.     

Stationary solutions in five-dimensional general relativity

Asymptotically Minkowskian stationary axisymmetric solutions of the five-dimensional Einstein equations are generated from particular classes of stationary axisymmetric solutions of the four-dimensional Einstein-Maxwell equations. First, the five-dimensional electrostatic and magnetostatic solutions are generated from the four-dimensional electrostatic solutions and a harmonic scalar field. Then, a new class of five-dimensional nonstatic solutions are generated from the four-dimensional class =+1. As an example, a three-parameter family of regular asymptotically flat rotating solutions is constructed. These solutions can be interpreted, after dimensional reduction to four dimensions, as extended elementary particles with mass, spin, electric charge, and magnetic dipole moment.     

Rotating colored black hole inSU(5) GUT

Gravity coupled to theSU(5) GUT is considered. A family of stationary axisymmetric solutions is obtained, which represents a rotating black hole with a QCD color hair as well as electromagnetic hairs.     

Distorted rotating black holes

An axisymmetric stationary metric which describes rotating black holes distorted by surrounding matter is presented by means of the inverse scattering problem technique, and is written down explicitly in terms of the Legendre polynomials. A mass formula for the distorted holes is derived via the Komar integrals over the horizon.     

Double Superpotential and Generation of New Solutions of Stationary Axisymmetric Gravitational Fields

In this paper COX’s superpotential is extended to double complex form firstly, then how to get hyperbolic complex superpotential from the known ordinary complex superpotential is discussed, finally, new solutions of stationary axisymmetric gravitational fields are shown with a few specific cases.     

Electromagnetic field properties in the vicinity of a massive wormhole

It is proved that not only massless but also traversable massive wormholes can have electromagnetic “hair.” An analysis is also presented of the passage from a traversable wormhole to the limit of a Reissner-Nordström black hole, with the corresponding disappearance of “hair.” A general method is developed for solving stationary axisymmetric Maxwell’s equations in the field of a massive, spherically symmetric wormhole. As a particular example of application of the method, a solution is found to the axisymmetric magnetostatic problem for a current loop in the field of the Bronnikov-Ellis-Morris-Thorne wormhole.