A new approach to general relativity by means of a tetrad or spinor formalism is presented. The essential feature of this approach is the consistent use of certain complex linear combinations of Ricci rotation coefficients which give, in effect, the spinor affine connection. It is applied to two problems in radiation theory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.

A new solution of the Einstein-Maxwell equations is presented. This solution has certain characteristics that correspond to a rotating ring of mass and charge.

It is shown that, in space-times which are asymptotically flat, there are reasonable physical restrictions that allow one to impose coordinate conditions (in addition to the usual Bondi-type conditions)which restrict the allowed coordinate group to a subgroup of the Bondi-Metzner-Sachs group. This subgroup is isomorphic to the improper orthochronous inhomogeneous Lorentz group.

It is shown that by means of a complex coordinate transformation performed on the monopole or Schwarzschild metric one obtains a new metric (first discovered by Kerr). It has been suggested that this metric be interpreted as that arising from a spinning particle. We wish to suggest a more complicated interpretation, namely that the metric has certain characteristics that correspond to a ring of mass that is rotating about its axis of symmetry. The argument for this interpretation comes from three separate places: (1) the metric appears to have the appropriate multipole structure when analyzed in the manner discussed in the previous paper, (2) in a covariantly defined flat space associated with the metric, the Riemann tensor has a circular singularity, (3) there exists a closely analogous solution of Maxwell's equations that has characteristics of a field due to a rotating ring of charge.

Recent work on the Bondi-Metzner-Sachs group introduced a class of functions sYlm(θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R3 and the properties of ð are derived from its relationship to an angular-momentum raising operator. The relationship of the sTlm(θ, φ) to the spherical harmonics of R4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.

A new class of empty-space metrics is obtained, one member of this class being a natural generalization of the Schwarzschild metric. This latter metric contains one arbitrary parameter in addition to the mass. The entire class is the set of metrics which are algebraically specialized (contain multiple-principle null vectors) such that the propagation vector is not proportional to a gradient. These metrics belong to the Petrov class type I degenerate.

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The asymptotic behavior of the Weyl tensor and metric tensor is investigated for probably all asymptotically flat solutions of the empty space Einstein field equations. The systematic investigation utilizes a set of first order differential equations which are equivalent to the empty space Einstein equations. These are solved asymptotically, subject to a condition imposed on a tetrad component of the Riemann tensor ψ0 which ensures the approach to flatness at spatial infinity of the space-time. If ψ0 is assumed to be an analytic function of a suitably defined radial coordinate, uniqueness of the solutions can be proved. However, this paper makes considerable progress toward establishing a rigorous proof of uniqueness in the nonanalytic case. A brief discussion of the remaining coordinate freedom, with certain topological aspects, is also included.