Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

WIMU instrumentation of assassin trainer & skeleton sled

Skeleton is a high‐speed Winter Olympic sport performed on the same twisting, downhill ice tracks used for Bobsleigh & Luge. The single rider sprints and pushes their sled for 20‐30m on a level start section before loading and going through a twisting course of over 1km, at speeds up to 140km/h, experiencing up to 5g. In competition, the top athletes can be within a fraction of a second of each other. The initial short pushing period is believed to be critical to overall performance but it is not well understood. A collaborative project between University of Bath, UK Sport and Tyndall National Institute is instrumenting skeleton athletes, training equipment and test tracks with Tyndall’s Wireless Inertial Measurement Unit technology in order to investigate and improve understanding of this phase of a skeleton run. It is hoped this will lead to improved training regimes and better performance of such elite, Olympic level athletes. This work presents an initial look at the system as implemented and data recorded.

WIMU instrumentation of assassin trainer & skeleton sled – initial data capture

Science Foundation Ireland (CSET - Centre for Science, Engineering and Technology, Grant No. 07/CE/11147)