Conformal diagrams for the gravitational collapse of a spherical dust cloud

Abstract

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.

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

References in corpus (7)

• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Spherical gravitational collapse in N-dimensions
• Cosmic Censorship in Higher Dimensions
• Cosmic Censorship in Higher dimension II
• Formation of naked singularities in five-dimensional space-time
• Cosmic Censorship for Self-Similar Spherical Dust Collapse
• Conformal diagrams for the gravitational collapse of a spherically symmetric dust cloud

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• Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
• The gravitational redshift of photons traversing a collapsing dust cloud and observable consequences
• Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices
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• Cauchy horizon stability in a collapsing spherical dust cloud I: geometric optic approximation and spherically symmetric test fields
• On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
• Cauchy horizon stability in a collapsing spherical dust cloud. II: Energy bounds for test fields and odd-parity gravitational perturbations
• Astrophysical Black holes: An Explanation for the Galaxy Quenching