Roy Kerr

• DSc
• Professor at University of Canterbury

Kerr-Schild metrics have been introduced as a linear superposition of the flat space-time metric and a squared null-vector field, say k, multiplied by some scalar function, say H. The basic assumption which led to Kerr solution was that k be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild Ansatz is revised by treating Ke...

This reprinting of a paper by Kerr and Schild, first published in 1965 in a conference volume that is difficult to get hold of today, has been selected by the Editors of General Relativity and Gravitation for publication in the Golden Oldies series of the journal. It is the only publication showing how the Kerr solution was originally arrived at. I...

Albert Einstein’s theory of general relativity describes the effect of gravitation on the shape of space and the flow of time. But for more than four decades after its publication, the theory remained largely a curiosity for scientists; however accurate it seemed, Einstein’s mathematical code—represented by six interlocking equations—was on...

Since it was first discovered in 1963 the Kerr metric has been used by relativists as a test‐bed for conjectures on worm‐holes, time travel, closed time‐like loops, and the existence or otherwise of global Cauchy surfaces. More importantly, it has also used by astrophysicists to investigate the effects of collapsed objects on their local environmen...

An historical account of the reasoning that led to the discovery of the Kerr and Kerr-Schild metrics in 1963-1964, and their physical interpretation as rotating black holes, is presented.

The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for a nonstationary case is obtained. We find a nonstationary shear free geodesic null congruence which is generated by a given analytical complex world line. Solu...

The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for a nonstationary case is obtained. We find a nonstationary shear free geodesic null congruence which is generated by a given analytical complex world line. Solu...

It is shown that, in the case where there is a single non-null Killing vector, the vacuum Einstein field equations imply that there is a Ricci collineation in the quotient 3-space. Using coordinates adapted to the collineation vector, we derive a fourth order partial differential equation involving the metric of the quotient 3-space and we show tha...

It is shown that the only empty space solution of the type flat space plus the square of a null vector whose singularities are confined to a bounded region is the Kerr metric.

In this paper, we construct all possible groups of motion (symmetry groups) for empty Einstein spaces admitting a diverging, geodesic, and shear-free ray congruence. (Minkowski space is excluded throughout the discussion.) It is proved that any such Einstein space cannot admit a symmetry group with dimension greater than four. Although the field eq...

It is shown that it is possible io set up a consistent Loreniz-invariant ; approximation procedure without it being necessary to expand the particle ; parameters, such as the mass and the charge. By using an invariant Green's ; function, an integral expression was calculated for the field. This is a ; solution of the Einstein-Maxwell field equation...

Algebraically degenerate solutions of the Einstein and Einstein‐Maxwell equations are studied. Explicit solutions are obtained which contain two arbitrary functions of a complex variable, one function being associated with the gravitational field and the other mainly with the electromagnetic field.

The Einstein field equations with incoherent matter are discussed for the case of homogeneous space‐time, i.e., for metrics allowing a four‐parametric, simply transitive group of motions. It is proved that the only universes satisfying the above are those of Einstein, Gödel, and Ozsvath.

From the integal form of the general solution for the retarded electromagnetic field of a localized chargecurrent distribution, the asymptotic field is shown to have the behavior F/sub mu nu //R + III/sub mu nu //R/sup 2/ + /sub 2/J/sub mu nu // R/sup 3/, where the coefficients satisfy N/sub nu mu /k/sup nu / = ), III/sub nu mu /k/sup nu / = Ak...

Algebraically special solutions of Einstein's empty-space field ; equations that are characterized by the existence of a geodesic and shear-free ; ray congruence are considered. A class of solutions is presented for which the ; congruence is diverging and is not necessarily hypersurface orthogonal. (C.E.S.);

The classifications of Einstein spaces by Schell and Petrov are combined and certain nonlocal results are obtained. In particular, we show that an Einstein space cannot be type I with a rank four Riemann tensor in a four‐dimensional region. On using the notion of a perfect or imperfect infinitesimal‐holonomy group, we establish the conditions under...

The metric tensor is constructed for Einstein spaces which are Petrov type III and whose holonomy group is four parametric. Together with the previously known plane fronted wave solutions, this completes the study of all metrics whose holonomy groups are less than six parameter. The Killing vector equations are studied and it is found that the spac...

Summary The three main methods used for solving the quasi-static field equations are discussed and it is shown that certain theorems have to be proved before it can be said that the physical equations of motion follow from the symmetry of the field around the sources. We have proved these results, and in the process have shown that there are seven...

The Lorentz-covariant approximation method for the field outside a set of localized particles has been analysed. It is found that as well as the usual equations of motion and energy derived by Eistein, Infeld and Hoffman for the quasi-static approximation, there are three further equations, the equations of spin, which must be satisfied by the stru...

In this paper, the methods of the first two papers of this series have been extended to the Einstein-Maxwell field. It is shown that it is possible to set up a consistent Lorentz-invariant approximation procedure without it being necessary to expand the particle parameters, such as the mass and the charge. By using an invariant Green’s function, we...

The equations of motion and spin are calculated to the second ; approximation by the Lorentz-covariant method in general relativity. The results ; are derived from the field outside the particle. (C.J.G.);