Stationary generalized Kerr-Schild spacetimes

In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike vector fields, from which some properties of the solutions are studied in a coordinate-free way. These spacetimes are algebraically special being their Petrov types II and D. This family includes all the classical vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves, and some other interesting solutions as, for instance, the Kerr metric in the background of the Einstein Universe. However, the family is much more general and depends on an arbitrary function of one variable.Comment: 21 pages, LaTeX 2.09. To be published in Journal of Mathematical Physic

Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^{\alpha} and w^{\alpha}

This is the third and last part of a series of 3 papers. Using the same method and the same coordinates as in parts 1 and 2, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity $u^{\alpha}$ and rotation $w^{\alpha}$ at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given.Comment: One missing piece, signaled after eq. (10.7), is added after (10.21). List of corrections: In (3.7) wrong subscript in vorticity; In (3.10) wrong subscript in last term of g_{23}; In (4.23) wrong formulae for g_{12} and g_{22}; In (7.17) missing factor in velocity; In (7.18) one wrong factor in g_{22}; In (10.9) factor in vorticity; In (10.15) - (10.20) y_0 = 0; In (10.20) wrong second term in y. The rewriting typos did not influence result

Twisting type-N vacuum fields with a group H2H_2

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two non-commuting Killing vectors. We study the case when the homothetic parameter $\phi$ takes the value -1, which is shown to admit a reduction to a third-order real ordinary differential equation for this problem, similar to that previously obtained by one of us when two Killing vectors are present.Comment: LaTeX, 11 pages. To be published in Classical and Quantum Gravit

Pure-radiation gravitational fields with a simple twist and a Killing vector

Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.Comment: revtex, 9 page

Rotating perfect fluid sources of the NUT metric

Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the vacuum exterior which consists only of a stationary region of the Taub-NUT space-time. The solution of the matching conditions leaves generally three parameters in the global solution. Examples of perfect fluid sources are discussed.Comment: 8 pages, late

New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Gra

Non-Abelian pp-waves in D=4 supergravity theories

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang-Mills connection on a self-dual metric and solving a Poisson equation for e^\phi. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page

Expanding, axisymmetric pure-radiation gravitational fields with a simple twist

New expanding, axisymmetric pure-radiation solutions are found, exploiting the analogy with the Euler-Darboux equation for aligned colliding plane waves.Comment: revtex, 5 page

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4