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

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, the authors 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. They derive several quantities, e.g., temperature, energy and entropic force. Their approach clearly exhibits that the entropic force on a smallest fundamental cell of holographic surface with radius r sub( 0) is halted. Accordingly, they 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.