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3 - Spherical collapse

Published online by Cambridge University Press:  15 August 2009

Pankaj S. Joshi
Affiliation:
Tata Institute of Fundamental Research, Mumbai, India
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Summary

A collapsing matter cloud, such as a massive star undergoing a continual gravitational collapse at the end of its life cycle, is modeled in general relativity as a dynamical spacetime geometry with a suitable energy–momentum tensor. The time evolution here is governed by the Einstein equations. The cloud has a boundary, with its interior collapsing continually as time evolves, and, at the boundary the interior spacetime is matched to a suitable exterior geometry so as to complete the full model of gravitational collapse. The physical situation considered here is that of the force of gravity being so overwhelming that no final, stable configuration, such as a neutron star or white dwarf, is possible as a collapse endstate, and a continual collapse inevitably proceeds. If the initial mass of the collapsing star is sufficiently high, then such a situation is realized.

In such a scenario, the classical theory leads the collapse to the formation of a spacetime singularity, as predicted by the singularity theorems of general relativity. The spacetime singularity is a region close to where the densities, spacetime curvatures, and all other physical quantities grow without bounds. At the singularity itself these are infinite, and hence, strictly speaking, the singularity is not part of the spacetime and is regarded as the boundary of the spacetime manifold. Eventually, as one moves closer to the singularity, the quantum gravity effects may dominate, which could resolve the classical singularity.

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Publisher: Cambridge University Press
Print publication year: 2007

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  • Spherical collapse
  • Pankaj S. Joshi, Tata Institute of Fundamental Research, Mumbai, India
  • Book: Gravitational Collapse and Spacetime Singularities
  • Online publication: 15 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511536274.004
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  • Spherical collapse
  • Pankaj S. Joshi, Tata Institute of Fundamental Research, Mumbai, India
  • Book: Gravitational Collapse and Spacetime Singularities
  • Online publication: 15 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511536274.004
Available formats
×

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

  • Spherical collapse
  • Pankaj S. Joshi, Tata Institute of Fundamental Research, Mumbai, India
  • Book: Gravitational Collapse and Spacetime Singularities
  • Online publication: 15 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511536274.004
Available formats
×