Newton's constant from a minimal length: Additional models

Abstract

We follow arguments of Verlinde and Klinkhamer, and construct two models of the microscopic theory of a holographic screen that allow for the thermodynamical derivation of Newton's law, with Newton's constant expressed in terms of a minimal length scale contained in the area spectrum of the microscopic theory. One of the models is loosely related to the quantum structure of surfaces and isolated horizons in loop quantum gravity. Our investigation shows that the conclusions reached by Klinkhamer regarding the new length scale seem to be generic in all their qualitative aspects.

7 pages, no figures. v2: removed various typos

References in corpus (3)

• Quantum Theory of Gravity I: Area Operators
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Counting black hole microscopic states in loop quantum gravity

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• Newtonian gravity as an entropic force: Towards a derivation of G
• Some aspects of entropic gravity in the presence of a noncommutative Schwarzschild-deSitter black hole
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• Newton's gravitational coupling constant from a quantum of area
• Thermodynamical features of Verlinde's approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales