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Newton’s constant from a minimal length: additional models. (English) Zbl 1208.83045

Summary: We follow arguments of E. P. Verlinde [On the Origin of Gravity and the Laws of Newton (2010); arXiv:1001.0785] and F. R. Klinkhamer [Newtonian gravity as an entropic force: Towards a derivation of G (2010); arXiv:1006.2094], 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 \(l\) 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 \(l\) seem to be generic in all their qualitative aspects.

MSC:

83C45 Quantization of the gravitational field
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C57 Black holes
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