Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Exact Solutions for Compact Objects in General Relativity

Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution. The generalisation involves the addition of anisotropic pressures and electric charge to the density profile. Of these new solutions three are found to obey all the necessary conditions of physical acceptability, including linear stability under radial perturbations, and causality of the speed of pressure waves inside the object. Additionally an equation of state can be found for all the physically viable solutions. The generalised pulsation equation for interior solutions to the EFE that include both electric charge and pressure anisotropy is derived and used to determine the stability of the solutions. However the pulsation equation found is general and can be used for all new solutions that contain these ingredients.Comment: 314 pages, PhD Thesis, defended on 12 April 2016. Separate chapters will be published subsequently as journal article