Modified Newtonian Dynamics as an Entropic Force

Abstract

Under natural assumptions on the thermodynamic properties of space and time with the holographic principle we reproduce a MOND-like behaviour of gravity on particular scales of mass and length, where Newtonian gravity requires a modification or extension if no dark matter component is introduced in the description of gravitational phenomena. The result is directly obtained with the assumption that a fundamental constant of nature with dimensions of acceleration needs to be introduced into gravitational interactions. This in turn allows for modifications or extensions of the equipartion law and/or the holographic principle. In other words, MOND-like phenomenology can be reproduced when appropriate generalised concepts at the thermodynamical level of space and/or at the holographic principle are introduced. Thermodynamical modifications are reflected in extensions to the equipartition law which occur when the temperature of the system drops below a critical value, equals to Unruh's temperature evaluated at the acceleration constant scale introduced for the description of the gravitational phenomena. Our calculations extend the ones by Verlinde [25] in which Newtonian gravity is shown to be an emergent phenomenon, and together with it reinforces the idea that gravity at all scales is emergent.

A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity

“…Using these results together with eqs. ( 57), ( 61), (25) and (62), we obtain that the only non vanish component of the tensor κ µν is κ 00 = 1/3. Finally, from eq.…”

“…In [1], a construction of an extended relativistic metric theory of gravity that recovers MOND on its weak field limit of approximation was made. This construction, has been tested to yield the correct bending angle of light for gravitational lensing in individual, groups and clusters of galaxies [60] as well as for the dynamics of clusters of galaxies [61] and for the accelerated expansion of the universe [62].…”

MOND and cosmological issues from entropic gravity and nonextensive thermostatistics correspondence

“…Verlinde considered entropy as the information relative to the positions of material bodies around a point mass M at a distance R. Besides, all points at this distance are useful to define a sphere S embedded into a D = 3 space. To sum up, when we change the bits of information that are localized on the screen, a force appears as a reaction to that modification [13][14][15][16][17]. This will be shown in eq.…”