Entropic force approach in a noncommutative charged black hole and the equivalence principle

TL;DR

This paper explores how entropic gravity in noncommutative charged black holes leads to black hole remnants that violate the equivalence principle, suggesting potential experimental tests of emergent gravity theories at small scales.

Contribution

It demonstrates that entropic force calculations in noncommutative black holes result in inert remnants with zero gravitational mass, challenging the equivalence principle.

Findings

Black hole remnants are inert and do not emit gravitational fields.

The equivalence principle is violated at the remnant scale.

Potential for experimental verification of entropic gravity at short distances.

Abstract

Recently, Verlinde has suggested a novel model of duality between thermodynamics and gravity which leads to an emergent phenomenon for the origin of gravity and general relativity. In this paper, we investigate some features of this model in the presence of noncommutative charged black hole by performing the method of coordinate coherent states representing smeared structures. We derive several quantities, e.g. temperature, energy and entropic force. Our approach clearly exhibits that the entropic force on a smallest fundamental cell of holographic surface with radius $r_0$ is halted. Accordingly, we can conclude that the black hole remnants are absolutely inert without gravitational interactions. So, the equivalence principle of general relativity is contravened due to the fact that it is now possible to find a difference between the gravitational and inertial mass. In other words, the gravitational mass in the remnant size does not emit any gravitational field, therefore it is experienced to be zero, contrary to the inertial mass. This phenomenon illustrates a good example for a feasible experimental confirmation to the entropic picture of Newton's Second law in very short distances.