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.

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.

Mariner II plasma and magnetic-field data are examined for explicit examples of low-frequency hydromagnetic waves. From the magnetic-field data, several sinusoidal waveforms are isolated. One of these clearly satisfies the hydromagnetic equations relating the magnetic-field variation to the ion-velocity perturbation for an Alfvén wave. This result is consistent with Barnes' theoretical prediction that only the Alfvén mode is not strongly damped in a plasma of moderate or high β.

A new coordinate system, intrinsically attached to an arbitrary timelike world line, is investigated in flat-space time. The Maxwell field tensor associated with the field of an arbitrarily moving charged particle assumes a particularly simple form in this, its intrinsic coordinate system. This reference frame is expected to be useful in General Relativity, in asymptotic studies of radiation, and equations of motion.

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