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2011

Lower bound on the spectral dimension near a black hole

Carlip, S., Grumiller, D.

Understand

We consider an evaporating Schwarzschild black hole in a framework in which the spectral dimension of spacetime varies continuously from four at large distances to a number smaller than three at small distances, as suggested by various approaches to quantum gravity.

  • We demonstrate that the evaporation stops when the horizon radius reaches a scale at which spacetime becomes effectively 3-dimensional, and argue that an observer remaining outside the horizon cannot probe the properties of the black hole at smaller scales.
  • This result is universal in the sense that it does not depend on the details of the effective dimension as a function of the diffusion time.
  • Observers falling into the black hole can resolve smaller scales, as can external observers in the presence of a cosmological constant.

Built on

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Similar

  • D. Grumiller, W. Kummer, and D. V. Vassilevich, Phys. Rept. 369

    2002

    Cited alongside, same era.

  • D. V. Vassilevich, Phys. Rept. 388

    2003

    Cited alongside, same era.

  • D. Grumiller, JCAP 05

    2004

    Cited alongside, same era.

  • J. Ambjorn, J. Jurkiewicz, and R. Loll, Phys. Rev. Lett. 95

    2005

    Cited alongside, same era.

  • S. Carlip (2009a), eprint 1009.1136

    Cited in the paper.

  • S. Carlip (2009b), eprint 0909.3329

    Cited in the paper.

Then

  • D. Grumiller and R. McNees, JHEP 04

    2007

    Later among the works it cites.

  • K. A. Stevens, K. Schleich, and D. M. Witt, Class. Quantun Grav. 26

    2009

    Later among the works it cites.

  • D. Grumiller and R. Jackiw, in Recent Developments in Theoretical Physics , edited by S. Gosh and G. Kar (World Scientific, Singapore, 2010), pp. 331–343, eprint 0712.3775

    2010

    Later among the works it cites.

  • J. Laiho and D. Coumbe (2011), eprint 1104.5505

    2011

    Closest in time.

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