Dietrich Kramer

Einstein-Maxwell solitons

The application of the inverse scattering method to the Einstein-Maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the Ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution.

A new solution for a rotating perfect fluid in general relativity

A new exact solution of Einsteins field equations with the energy-momentum tensor of a perfect fluid is given. This solution can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure. The fluid rotates rigidly; the equation of state is epsilon +3p=constant. The solution is of Petrov type D and admits a maximal group G2 of motions.

Pure and gravitational radiation

The well-known treatment of asymptotically flat vacuum fields is adapted to pure radiation fields. In this approach we find a natural normalization of the radiation null vector. The energy balance at null infinity shows that the mass loss results from a linear superposition of the pure and the gravitational radiation parts. By transformation to Bondi-Sachs coordinates the Kinnersley photon rocket is found to be the only axisymmetric Robinson-Trautman pure radiation solution without gravitational radiation.

Equivalence of various pseudopotential approaches for Einstein-Maxwell fields

In the literature, various systems of liner eigenvalue equations from which the Einstein-Maxwell equations for stationary axisymmetric exterior fields follow as the integrability conditions were derived. In the present paper, these linear systems are shown to be equivalent; the explicit transformations mapping one form to another are given.

Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. The prolongation structure in the spirit of Wahlquist and Estabrook (1975)) of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found.

Two Kerr-NUT constituents in equilibrium

The equilibrium conditions for the superposition of two Kerr-NUT solutions are revisited. The new derivation of these conditions leads to formulas which include also the hyperextreme case. In the symmetric model of two hyperextreme constituents [3–5,8] the surfacef=0 of infinite red shift is investigated. It turns out that, for large enough distance parameter, the surfacef=0 consists of disconnected parts surrounding each source separately.

A rotating pure radiation field

Starting with the Kerr solution, we generate an algebraically special pure radiation solution of Einsteins field equations. This solution is axisymmetric, asymptotically flat and regular on the axis. The metric is determined up to a linear second-order ordinary differential equation for which only particular solutions are known. The transformation to Bondi--Sachs coordinates is determined as a power series expansion in terms of the inverse radial coordinate. The relation between our derivation and another approach using Cauchy--Riemann structures is established and the underlying Cauchy--Riemann structure of our solution is given.

Perfect fluids with conformal motion

The axisymmetric rigidly rotating or static perfect fluid solutions admitting a proper conformai Killing vector orthogonal to the orbits of the two-dimensional group of motions are determined.

A new inhomogeneous cosmological model in general relativity

A new perfect fluid solution of Einsteins field equations is explicitly given; it is in general of Petrov type II and admits a maximal group of G2 of motions. The hypersurface-normal four-velocity is not orthogonal to the group orbits. The equation of state is w=p+constant. The solution can be interpreted as an axisymmetric gravitational field, and appears to represent an inhomogeneous cosmological model. The nature of the singularities is studied.

Two Counter-moving Light Beams

The cylindrically symmetric field of two beamsof light shining in opposite directions is studied. Wepresent four static or stationary exact solutions of thecorresponding field equations and compare their properties.