Exact Fermi coordinates for a class of spacetimes

We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative cosmological constant, and the Einstein static universe. Maximal charts for Fermi coordinates are discussed.Comment: 15 page

Frame dragging anomalies for rotating bodies

Examples of axially symmetric solutions to Einstein's field equations are given that exhibit anomalous "negative frame dragging" in the sense that zero angular momentum test particles acquire angular velocities in the opposite direction of rotation from the source of the metric.Comment: This version adds minor clarifications to the original published version of this paper, which among other things remove the source of Culetu's objections in arXiv:0811.4592. In addition, a reference is added with further acknowledgment

General Transformation Formulas for Fermi-Walker Coordinates

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.Comment: 23 pages. Corrected typos in the last two equations. Accepted for publication in Classical and Quantum Gravit

Patient-specific image-based computer simulation for theprediction of valve morphology and calcium displacement after TAVI with the Medtronic CoreValve and the Edwards SAPIEN valve

AIMS: Our aim was to validate patient-specific software integrating baseline anatomy and biomechanical properties of both the aortic root and valve for the prediction of valve morphology and aortic leaflet calcium displacement after TAVI. METHODS AND RESULTS: Finite element computer modelling was performed in 39 patients treated with a Medtronic CoreValve System (MCS; n=33) or an Edwards SAPIEN XT (ESV; n=6). Quantitative axial frame morphology at inflow (MCS, ESV) and nadir, coaptation and commissures (MCS) was compared between multislice computed tomography (MSCT) post TAVI and a computer model as well as displacement of the aortic leaflet calcifications, quantified by the distance between the coronary ostium and the closest calcium nodule. Bland-Altman analysis revealed a strong correlation between the observed (MSCT) and predicted frame dimensions, although small differences were detected for, e.g., Dmin at the inflow (mean±SD MSCT vs. MODEL: 21.6±2.4 mm vs. 22.0±2.4 mm; difference±SD: -0.4±1.3 mm, p<0.05) and Dmax (25.6±2.7 mm vs. 26.2±2.7 mm; difference±SD: -0.6±1.0 mm, p<0.01). The observed and predicted calcium displacements were highly correlated for the left and right coronary ostia (R2=0.67 and R2=0.71, respectively p<0.001). CONCLUSIONS: Dedicated software allows accurate prediction of frame morphology and calcium displacement after valve implantation, which may help to improve outcome

A Statistical Mechanical Problem in Schwarzschild Spacetime

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief comments on the system's center of mass and the thermodynamic limi