Modified Newton's gravity law in Verlinde formalism based on an extended microstructure

This paper analyses the effects of an extended microstructure in the microscopic discretion of spacetime. In this setup, all point structures get replaced by smeared distributions owing to this extended microstructure. We investigate the effect that such a modification of point mass and charge has on the thermodynamics of a charged anti-de Sitter black hole. In addition, the modification of point structures by smeared distributions modifies the energy of the black hole. The effects of such a deformation in the macroscopic geometry are studied by using the local equipartition of energy and the holographic principle. Thus, it is possible to obtain the corrections to the entropic force from such a deformation of the theory. This will in turn modify the Newton's gravity law in the Verlinde formalism.