Geometric analysis of particular compactly constructed time machine spacetimes

We formulate the concept of time machine structure for spacetimes exhibiting a compactly constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by Ori, we present an analysis of its geodesics analogous to the one conducted in the case of the Schwarzschild spacetime. We conclude that the pseudo Schwarzschild spacetime is geodesically incomplete and not extendible to a complete spacetime. We then introduce a rotating generalization of the pseudo Schwarzschild metric, which we call the pseudo Kerr spacetime. We establish its time machine structure and analyze its global properties.