Implications of Maximum Acceleration on Dynamics

Abstract

Considering the corrected Unruh temperature as well as the entropic force perspective of gravity, we are able to derive the modification of the Newton's law of gravity. In addition, we also investigate the effects of the highest achievable acceleration correction to the Unruh temperature on the Poisson equation. Moreover, we address modifications to the Newtonian cosmology as well as the Friedmann equations corresponding to the upper bound for acceleration.

Energy Definition and Dark Energy: A Thermodynamic Analysis

“…which clearly differs from (5) unless we have a pressureless fluid [41,47]. Although this energy definition has originally been obtained by using the Einstein field equations [47], it is in accordance with various thermodynamic and holographic approaches [34][35][36][37][38][39][40][41][42][43][44][45][46]. In fact, if we accept this energy definition as a basic equation and not a secondary equation [34][35][36][37], then there are various thermodynamic and holographic approaches employed to get the Friedmann and gravitational field equations in various theories by using the Komar mass definition [34][35][36][37][38][39][40][41][42][43][44][45][46].…”

“…A thermodynamic analysis can also lead to a better understanding of the origin of dark energy, responsible for the current accelerated universe [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In fact, there are thermodynamic and holographic approaches claiming that the cosmos expansion can be explained as an emergent phenomenon [18,[34][35][36][37][38][39][40][41][42][43][44][45][46]. Two key points in these approaches are the definition of energy and the form of the energy-momentum conservation law [14,19,[34][35][36][37][38], and indeed, their results are so sensitive to the energy definitions that have been employed [19].…”

“…ii) We also showed the form of energy-momentum conservation law depends on the energy definition, and if one uses the Komar mass, then KCL is obtained instead of OCL. iii) The Komar mass is the backbone of some holographic and thermodynamic attempts to obtain field equations of various gravitational theory [34][35][36][37][38][39][40][41][42][43][44][45][46] motivating us to use KCL instead of OCL. iv) Observational data admit the break-down of OCL in the current accelerated era [48].…”

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

“…It is important to note that the entropy expression plays a crucial role in this theory. In fact, diverse corrections to the entropy-area relation presents various modifications to the gravitational theories and their corresponding cosmology [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. It has also been shown [23][24][25][26][27] that if the Unruh temperature [29] is attributed to the holographic screen, then the quantum statistics of surface degrees of freedom may help us in obtaining a theoretical basis for the Modified Newtonian Dynamics (MOND) theory [30][31][32].…”

A Tsallisian Universe

“…An astonishing approach which attracts investigators to itself [53][54][55][56][57][58][59][60][61][62][63][64][65]. In the framework of generalized entropies, Verlinde hypothesis leads to significant implications on the cosmic evolution [66][67][68][69], Newtonian gravity [70], Jeans mass (as a stability criterion) [71], and also gravitational systems [72][73][74][75][76][77]. Indeed, differences between generalized entropies and Bekenstein entropy, originated from the non-extensive viewpoint, can i) describe the universe inflationary phases [32][33][34]39], ii) relate Padmanabhan emergent gravity scenario to the Verlinde hypothesis [32], and iii) propose an origin for MOND theory [70].…”