Conformal diagrams for the gravitational collapse of a spherical dust cloud

Details Conformal diagrams for the gravitational collapse of a spherical dust cloud Conformal diagrams for the gravitational collapse of a spherical dust cloud

2011-06-13

arxiv.org/abs/1106.2504v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

added a new subsection with a phase space analysis, 23 pages, 8 figures

Scientific paper

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of the radial null geodesics and a local analysis of their behavior close to the singularity. As an application, we consider a collapsing spherical dust cloud, generate the corresponding conformal diagram and analyze the structure of the resulting singularity. A new bound on the initial data which guarantees that the singularity is visible from future null infinity is also obtained.

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