Lower bound on the spectral dimension near a black hole
- Department of Physics, University of California, Davis, California 95616 (United States)
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
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 three-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. Even in these cases, though, we obtain an absolute bound D{>=}2 on the effective dimension that can be seen in any such attempt to measure the properties of the black hole.
- OSTI ID:
- 21607912
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 84, Issue 8; Other Information: DOI: 10.1103/PhysRevD.84.084029; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Black hole evaporation and compact extra dimensions
Black hole thermodynamics from near-horizon conformal quantum mechanics