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.

Mícheál Coimín agus a shaothar

Is é a chuirim romham a dhéanamh sa tráchtas seo ná eagar a chur ar shaothar liteartha Mhíchíl Coimín; file agus údar próis a bhí ag saothrú na litríochta i gCill Chorcoráin, Contae an Chláir san ochtú haois déag. D’éag sé sa bhliain 1760 nuair a bhí sé beagnach 90 bliain d’aois. Is féidir a rá go bhfuil an Coimíneach, ó thaobh chanóin litríocht na Gaeilge de i measc na mionscríbhneoirí, agus níl aon dabht faoi ach go bhfuil an-chuid de léitheoirí na Gaeilge sa lá atá inniu ann dall ar a chuid scríbhneoireachta. Tá cáil air mar údar ‘Laoi Oisín i dTír na n-Óg’ ach mar a léireofar sa tráchtas seo, tá gach cuma ar an scéal nárbh é a scríobh. Tá againn óna pheann dornán beag dánta agus dhá scéal rómánsaíochta (‘Eachtra Thoroilbh Mhic Stairn’ agus ‘Eachtra a Thriúr Mac’) a scríobh sé nuair a bhí an traidisiún sin próis ar an dé deiridh. Níl aon chuid dá shaothar ar fáil in eagráin a shásódh léitheoirí an lae inniu ná na critéir scolártha atá i bhfeidhm anois. Níor tháinig aon lámhscríbhinn, i lámh an Choimínigh, anuas chugainn agus dá bhrí sin bhí dúshlán áirithe ag baint leis an bpróiseas eagarthóireachta. Sa tráchtas rinne mé an suirbhé is iomláine go dtí seo ar a shaothar i dtraidisiún na lámhscríbhinní agus ar na scríobhaithe a rinne é a sheachadadh. Bhí sé mar aidhm agam teacht ar na lámhscríbhinní is údarásaí sa traidisiún d’fhonn eagráin a réiteach a bheadh dílis dá bhunshaothar. Chomh maith leis sin tabharfar cuntas ar a bheatha agus ar a chúlra liteartha, agus déanfar iniúchadh criticiúil ar a shaothar próis agus fileata.