Junction Conditions and Thin Shells in General Relativity Using Computer Algebra

Details Junction Conditions and Thin Shells in General Relativity Using Computer Algebra Junction Conditions and Thin Shells in General Relativity Using Computer Algebra

Nov 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt........18m&link_type=abstract

Thesis (PHD). QUEEN'S UNIVERSITY AT KINGSTON (CANADA) , Source DAI-B 58/05, p. 2470, Nov 1997, 132 pages.

Computer Science

Spacetime

Scientific paper

This thesis examines the subject of developing a computer tool to aid reseachers in joining solutions to Einstein's equations. Research in general relativity has benefited from the existence of computer tools to calculate e.g. curvature tensors and scalars. No such tools exist for evaluating the junction conditions required to join two spacetimes. The result has been that the majority of junctions studied in the literature We then use GRJunction to study a number of new non-spherical timelike rely on spherical symmetry (or small deviations from it). We describe the development of GRJunction, a package to perform junction calculations. The development of the package requires a careful analysis of the junction formalism to ensure the process is as algorithmic as possible. We verify GRJunction by repeating a number of analyses in the literature. and null shell configurations. We present a spherical shell as an approximate source for the Curzon spacetime. We show how two Kerr solutions can be joined in the slow rotation approximation along both timelike and null shells. The exact joining of two Kerr-Newman solutions along their respective event horizons is also presented. Timelike non-spherical thin shell wormholes are discussed. The dynamics of non-spherical timelike surfaces are considerably different from the existing spherical cases which have been presented in the literature. The velocity of the shell can appear in the intrinsic metric of the shell and the evolution of the shell is required in order to fully specify its geometry. These analyses demonstrate the utility of a tool like GRJunction.

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