Quantum corrected spherical collapse: A phenomenological framework

Jonathan Ziprick and Gabor Kunstatter
Phys. Rev. D 82, 044031 – Published 13 August 2010

Abstract

A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter “piles up” on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.

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  • Received 16 April 2010

DOI:https://doi.org/10.1103/PhysRevD.82.044031

© 2010 The American Physical Society

Authors & Affiliations

Jonathan Ziprick*

  • Perimeter Institute and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Gabor Kunstatter

  • Department of Physics and Winnipeg Institute of Theoretical Physics, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9

  • *jziprick@perimeterinstitute.ca
  • g.kunstatter@Uwinnipeg.ca

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Vol. 82, Iss. 4 — 15 August 2010

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