Can Entropic Force Law Contravene the Equivalence Principle of General Relativity?

Details Can Entropic Force Law Contravene the Equivalence Principle of General Relativity? Can Entropic Force Law Contravene the Equivalence Principle of General Relativity?

2011-11-10

arxiv.org/abs/1111.2468v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures, new references added, minor revision

Scientific paper

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 negative entropic force, i.e. gravitational repulsive force and that is worth of mentioning: at this regime either our analysis is not the proper one, or non-extensive statistics should be employed.

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