Boosting the Kerr metric

An exact solution of Einstein's equations describing the gravitational wave associated to a ring of massless particles is presented. It has been obtained by boosting the Kerr metric along the axis of symmetry, and considering the limit in which the speed of the boost tends to the velocity of light.     

Causality violation in the Kerr metric

The conjecture that geodesics in the Kerr matric witha > m cannot violate causality in the sense of meeting a turning point before making up for lost time, is found to be untrue for null geodesics.     

De/re-constructing the Kerr metric

We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately, we transform the Kerr metric to Schwarzschild frame to exhibit its limits in that familiar setting.     

Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

Microgeon with a Kerr metric

The structure of electromagnetic and gravitational fields near the singular ring of the Kerr metric is analyzed. An approximate joint solution of the system of Maxwell-Einstein equations is given for a metric with the parameters of an electron; this solution describes a microgeon, a model of an electron. A new interpretation of the two-sheet nature of the Kerr metric is given.     

Kerr metric in eight dimensions

A Kerr-type metric is constructed in eight dimensions using the octonionic structure constants.     

An “interior” of the Kerr metric

We show that the Kerr solution may be interpreted as arising form a thin rigidly rotating disk with a regular interior and a singular rim. The surface stress-energy tensor in the interior of the disk represents a fictitious material with positive isotropic stress and zero energy density.     

The Kerr metric in cosmological background

A metric satisfying Einstein’s equations is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a homogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.     

A note on the derivation of the Kerr metric

An elementary derivation of the Kerr solution of Einstein's empty field equations is described.     

Ellipsoidal space-times,sources for the Kerr metric

The paper develops a systematic derivation of the Kerr metric and its possible sources in a clear geometric manner. It starts with a concise account of previous attempts at constructing an interior Kerr solution. Then a treatment of stationary-axisymmetric spacetimes, specially fitted to the needs of the following analysis, is presented. A new notion of an ellipsoidal space-time is introduced: it is a space-time in which local rest 3-spaces of some observers split naturally into congruences of concentric and coaxial ellipsoids. It is shown that these 3-spaces are natural spaces to consider the ellipsoidal figures of equilibrium. The investigation is carried out in detail for axially symmetric oblate confocal ellipsoids, but possible generalizations are indicated. The Kerr metric is found to be an ellipsoidal space-time of this special kind. Some remarks concerning an (unfound) explicit interior Kerr solution conclude the paper.     

Numerical calculation of bound geodesics in the Kerr metric

Timelike geodesics, especially bound orbits in the equatorial plane (?=π/2) and spherical orbits (r=const), are calculated numerically. We plot the orbits using the Kerr-Schild coordinate system. The periastron advance and the dragging of nodes have the same values in any coordinate system and can be directly measured by an observer at infinity.     

A newtonian model of the source of the Kerr metric

A complete newtonian model of the source of the gravitational field whose equipotential surfaces are confocal revolution ellipsoids is presented. The solution exhibits a singularity familiar from the Kerr metric.     

Stationary axisymmetric test fields on a Kerr metric

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

Black holes: a physical route to the Kerr metric

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole. In this paper I discuss the possibility of a quasi–stationary transition from rotating equilibrium configurations of normal matter to rotating bla ck holes.     

Time machine and geodesic motion in Kerr metric

The existence of nontrivial causality violation is a peculiar property of the space-time around a naked singularity. In the case of Kerr metric witha > m we have found that for a particular class of geodesies that could in principle violate causality, the conditions for causality violation are never satisfied.On leave of absence from Institute of Astronomy, Polish Academy of Sciences, Warsaw, Poland.