Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

Closed Time-like Curves and Inertial Frame Dragging: How to Time Travel via Spacetime Rotation

As the number of solutions to the Einstein equations with realistic matter sources that admit closed time-like curves (CTC's) has grown drastically, it has provoked some authors [10] to call for a physical interpretation of these seemingly exotic curves that could possibly allow for causality violations. A first step in drafting a physical interpretation would be to understand how CTC's are created because the recent work of [16] has suggested that, to follow a CTC, observers must counter-rotate with the rotating matter, contrary to the currently accepted explanation that it is due to inertial frame dragging that CTC's are created. The exact link between inertialframe dragging and CTC's is investigated by simulating particle geodesics and the precession of gyroscopes along CTC's and backward in time oriented circular orbits in the van Stockum metric, known to have CTC's that could be traversal, so the van Stockum cylinder could be exploited as a time machine. This study of gyroscopeprecession, in the van Stockum metric, supports the theory that CTC's are produced by inertial frame dragging due to rotating spacetime metrics.