Entropic force, noncommutative gravity and ungravity

TL;DR

This paper explores how entropic force concepts can be extended to include quantum gravity corrections like noncommutative geometry and ungravity, revealing deviations from Newton's law and insights into spacetime thermodynamics.

Contribution

It extends Verlinde's entropic gravity derivation to incorporate various quantum gravity effects, demonstrating the robustness of the approach under these modifications.

Findings

Noncommutative geometry deviations mimic thermodynamic temperature effects.

Noncommutative character of spacetime relates to thermodynamic temperature.

Verlinde's derivation remains valid with multiple quantum gravity corrections.

Abstract

After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.