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

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.

Noncommutative Wormholes in f(R) Gravity with Lorentzian Distribution

“…We are trying to solve the field equations given above in non-commutative geometry with Lorentzian distribution. Here we take the energy density of the static and spherically symmetric smeared and particle-like gravitational source of the following [12] …”

“…They showed that in their model, the energy conditions are satisfied in the desired range of radial coordinate. We here perform a similar analysis of [11] however, taking into account a Lorentizian density distribution of a point gravitational source [12]. We derive the wormhole's solutions in two possible schemes for a given Lorentzian distribution: assuming an astrophysically viable F (R) function such as a power-law form :F (R) = aR m and have discussed several solutions corresponding to different values of the exponential parameter.…”

Two particle entanglement and its geometric duals

“…(7), (9), (13) and (14) P, S and Q of the two particles depend on 1 + 6 dimensions, 6 space dimensions with a single time coordinate. One can define…”

“…Thus it naturally led many physicists to the attempt to reformulate quantum mechanics in a geometric language, like GR. References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are a few such efforts towards the geometrical rewriting of quantum laws.…”

Geometric description of the Schrödinger equation in (3n+1)-dimensional configuration space

“…It is thus natural that there are numerous attempts to reformulate quantum mechanics in a more geometrical way [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”