Stationary axisymmetric spacetimes containing a pair of oppositely rotating periodically intersecting circular geodesics allow us to study the various socalled 'clock effects' by comparing either observer or geodesic proper time periods of orbital circuits defined by the observer or the geodesic crossing points. This can be extended from a comparison of clocks to a comparison of parallel-transported vectors, leading to the study of special elements of the spacetime holonomy group. The band of holonomy invariance found for a dense subset of special geodesic orbits outside a certain radius in the static case does not exist in the nonstatic case. In the Kerr spacetime the dimensionless frequencies associated with parallel-transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics. PACS number: 0420C−1/2 ii ∂ i be the orthonormal frame vectors along the time slices (to be referred to as the 'spherical frame'), where i = r, θ, φ. ∂ t and ∂ φ are Killing vector fields associated respectively with stationarity and axisymmetry; ∂ φ has closed orbits φ : 0 → 2π. All considerations below will be limited to the region of spacetime where the one-form dt remains timelike and this lapse-shift decomposition remains valid, namely, outside the (outer) horizon r = r + in the Kerr spacetime, the (outer) surface where N = (−g tt ) −1/2 → 0. Static spacetimes occur as the special case g tφ = 0 = N φ . Explicit values of the various metric quantities for the Kerr spacetime are given in table 1 of [3].

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A method is presented for the interpolation of optimally 'smooth' background correction matrices within arbitrarily shaped boundaries. Practical means of implementing this technique are discussed, along with series expansions for the special cases of square and round boundaries. This class of interpolation methods has the advantages over previous techniques of providing a unique mathematical solution, connecting exactly to count rates on the boundary, and containing no singularities. Clinical scintigraphic images and mathematically generated surfaces are used to test the different cases of the method, and it is shown that confining the boundary to a circle produces the most rapid convergence with the minimum deviation from ideal surfaces. Under common clinical conditions, these techniques lend themselves well to automated, non-interventional computer processing.

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