No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

The Flatter Regions of Newman, Unti, and Tamburino's Generalized Schwarzschild Space

### Abstract

The ``generalized Schwarzschild'' metric discovered by Newman, Unti, and Tamburino, which is stationary and spherically symmetric, is investigated. We find that the orbit of a point under the group of time translations is a circle, rather than a line as in the Schwarzschild case. The time‐like hypersurfaces *r* = const which are left invariant by the group of motions are topologically three‐spheres *S* ^{3}, in contrast to the topology*S* ^{2} × *R* (or *S* ^{2} × *S* ^{1}) for the *r* = const surfaces in the Schwarzschild case. In the Schwarzschild case, the intersection of a spacelike surface *t* = const and an *r* = const surface is a sphere *S* ^{2}. If σ is any spacelike hypersurface in the generalized metric, then its (two‐dimensional) intersection with an *r* = const surface is not any closed two‐dimensional manifold, that is, the generalized metric admits no reasonable spacelike surfaces. Thus, even though all curvature invariants vanish as *r* → ∞, in fact *R* _{μναβ} = *O*(1/*r* ^{3}) as in the Schwarzschild case, this metric is not asymptotically flat in the sense that coordinates can be introduced for which *g* _{μν} − η_{μν} = *O*(1/*r*). An apparent singularity in the metric at small values of *r*, which appears to be similar to the spurious Schwarzschild singularity at *r* = 2*m*, has not been studied. If this singularity should again be spurious, then the ``generalized Schwarzschild'' space would represent a terminal phase in the evolution of an entirely nonsingular cosmological model which, in other phases, contains closed spacelike hypersurfaces but no matter.

© 1963 The American Institute of Physics

Received 17 December 1962
Published online 22 December 2004