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Initial value formalism for Lemaitre-Tolman-Bondi collapse

Published online by Cambridge University Press:  17 February 2009

P. D. Lasky ,
A. W. C. Lun  and
R. B. Burston
P. D. Lasky
Affiliation:
Centre for Stellar and Planetary Astrophysics School of Mathematical Sciences Monash UniversityWellington Rd Melbourne 3800 Australia; [email protected]
A. W. C. Lun
Affiliation:
Centre for Stellar and Planetary Astrophysics School of Mathematical Sciences Monash UniversityWellington Rd Melbourne 3800 Australia; [email protected]
R. B. Burston
Affiliation:
2Max Planck Institute for Solar System Research37191 Katlenburg-Lindau Germany
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Formulating a dust-filled spherically symmetric metric utilizing the 3 + 1 formalism for general relativity, we show that the metric coefficients are completely determined by the matter distribution throughout the spacetime. Furthermore, the metric describes both inhomogeneous dust regions and also vacuum regions in a single coordinate patch, thus alleviating the need for complicated matching schemes at the interfaces. In this way, the system is established as an initial boundary value problem, which has many benefits for its numerical evolution. We show the dust part of the metric is equivalent to the class of Lemaitre-Tolman-Bondi (LTB) metrics under a coordinate transformation. In this coordinate system, shell crossing singularities (SCS) are exhibited as fluid shock waves, and we therefore discuss possibilities for the dynamical extension of shell crossings through the initial point of formation by borrowing methods from classical fluid dynamics. This paper fills a void in the present literature associated with these collapse models by fully developing the formalism in great detail. Furthermore, the applications provide examples of the benefits of the present model.

Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 53 - 73
Copyright
Copyright © Australian Mathematical Society 2007

References

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