Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

Low grade metamorphism of the Manx Group, Isle of Man; a comparative study of white mica 'crystallinity' techniques

Studies have been made in two laboratories on metapelites from the Manx Group, Isle of Man, showing the distribution of white mica ‘crystallinity’, using the Kubler index (Δ°2Θ) and the Weber index (Hbrel). Two isocryst maps, which show broadly similar distributions of metamorphic grade, are illustrated and a correlation between the laboratories is presented. The mineralogy of the <2 m fraction in relation to ‘crystallinity’ has been determined. The distribution of metamorphic grade over central and eastern parts of the Isle of Man, as depicted by the Kubler index isocryst map, is related to subjacent granite plutons, but these contact metamorphic effects overprint an earlier, largely anchizonal, regional metamorphism. Localized, late, retrograde effects are related to low temperature hydrothermal mineralization and to cold re-working in a large fault zone. Differences between the maps are largely in the degrees of resolution which stem directly from the different sampling intervals employed. Comparisons between the maps suggest a sampling interval of 1-2 km is adequate in regions of simpler geology; but that an interval of <1 km may be necessary in more complex regions. Well resolved maps can be produced only when the sampling interval is linked to geology. The changes in the mineralogy of the <2 m fraction in relation to grade are closely similar to those described from Lower Palaeozoic metapelites from North Wales, although higher grades have been reached in the Manx Group with the development of biotite