Spacetimes admitting a three-parameter group of isometries and quasilocal gravitational mass

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Abstract
Spacetimes admitting a three-parameter group of motions multiply transitive on two-dimensional spacelike orbits allow construction of a simple geometrical invariant out of the magnitudes of Killing fields, their gradients, and the metric. We show that this invariant covariantizes and geometrizes certain forms of "quasilocal mass" introduced and discussed in the literature, in particular, Misner's mass in spherical symmetry and Taub's "mass" in plane symmetry.