A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

Abstract

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy-momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy-momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples we consider the energy-momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.

7 pages, LaTex; this essay received an "honorable mention" in the 2004 Essay Competition of the Gravity Research Foundation; submitted to IJMPD on 23 June 2004; published as Int.J.Mod.Phys.D13:2337-2343,2004

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• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Black Hole Remnants and Dark Matter

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