Einstein equations and MOND theory from Debye entropic gravity

Abstract

Verlinde's proposal on the entropic origin of gravity is based strongly on the assumption that the equipartition law of energy holds on the holographic screen induced by the mass distribution of the system. However, from the theory of statistical mechanics we know that the equipartition law of energy does not hold in the limit of very low temperature. Inspired by the Debye model for the equipartition law of energy in statistical thermodynamics and adopting the viewpoint that gravitational systems can be regarded as a thermodynamical system, we modify Einstein field equations. We also perform the study for Poisson equation and modified Newtonian dynamics (MOND). Interestingly enough, we find that the origin of the MOND theory can be understood from Debye entropic gravity perspective. Thus our study may fill in the gap existing in the literature understanding the theoretical origin of MOND theory. In the limit of high temperature our results reduce to their respective standard gravitational equations.

Implications of the generalized entropy formalisms on the Newtonian gravity and dynamics

“…By applying our analysis to the galaxies rotation curves, one can identify in a natural way a e with a 0 ≃ 10 −10 m/s 2 , which is analogous to the Milgrom's MOND acceleration [30][31][32]. It has been argued that since the holographic screen, assumed in previous section, can be considered as the system boundary [7,23,24], one can attribute Unruh temperature [29]…”

“…Now, bearing the ∆S ∆x = ( 1 ηλm ) dS dA and λ m = 1 m relations in mind, by inserting Eqs. (23) and (24) into Eq. (8) and using Eq.…”

“…(26), and its value is not necessarily the same for all the galaxies. For example, if a 0 ≃ 10 −10 m/s 2 [24,[30][31][32], then we can use Eq. (26) in order to find δ (or equally q) for a system with mass M .…”

q-deformed Einstein equations from entropic force

“…Moreover, in the Ref. [9], the modified Einstein equations were attained by considering the Debye correction to the equipartition law of energy in the framework entropic gravity scenario. As a consequence, the results in this study have different properties from these studies in the literature [9,14,16].…”

Implications of Maximum Acceleration on Dynamics

“…Let us compare the result obtained here with the modified Newtonian dynamics (MOND) resulting from Deby entropic gravity [53]. It was argued that by adopting Debye correction to the equipartition law of energy in the framework of entropic gravity scenario, it is possible to understand the theoretical origin of the MOND theory [53,54]. According to the MOND theory, the Newton's law of gravity is modified as,…”