Analytical Modeling of Metal Oxide Semiconductor Inversion-Layer Capacitance

Abstract

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].