Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas

TL;DR

This paper explores the entropic force approach to noncommutative Schwarzschild black holes, revealing the failure of the equivalence principle and unusual dynamical features at small scales, challenging current physical ideas.

Contribution

It generalizes the entropic force model to noncommutative black holes using smeared mass distributions, uncovering inert black hole remnants and violations of the equivalence principle.

Findings

Entropic force vanishes at the smallest holographic unit.

Black hole remnants are inert, with no gravitational interaction.

Unusual dynamics like repulsive gravity and negative energy occur at small scales.

Abstract

Recently, a new perspective of gravitational-thermodynamic duality as an entropic force arising from alterations in the information connected to the positions of material bodies is found. In this paper, we generalize some aspects of this model in the presence of noncommutative Schwarzschild black hole by applying the method of coordinate coherent states describing smeared structures. We implement two different distributions: (a) Gaussian and (b) Lorentzian. Both mass distributions prepare the similar quantitative aspects for the entropic force. Our study shows, the entropic force on the smallest fundamental unit of a holographic screen with radius $r_0$ vanishes. As a result, black hole remnants are unconditionally inert even gravitational interactions do not exist therein. So, a distinction between gravitational and inertial mass in the size of black hole remnant is observed, i.e. the failure of the principle of equivalence. In addition, if one considers the screen radius to be less than the radius of the smallest holographic surface at the Planckian regime, then one encounters some unusual dynamical features leading to gravitational repulsive force and negative energy. On the other hand, the significant distinction between the two distributions is conceived to occur around $r_0$, and that is worth of mentioning: at this regime either our analysis is not the proper one, or non-extensive statistics should be employed.