The other way around: from alternative gravity to entropy

Abstract

Since the seminal work of Verlinde, the idea that gravity may be an emergent force of entropic origin has gained widespread attention. Many generalizations of this key idea have been considered in the literature, starting from well-known and well-motivated generalized entropies to derive generalized gravity theories. Here, we approach the problem from the opposite direction. We ask whether phenomenologically motivated generalized gravitational theories, yet lacking a strong theoretical justification, may find their origin in an entropic scenario. We examine a set of seven proposals of modified gravity, which have been introduced either (i) as large-scale corrections to Newtonian gravity, aimed at reproducing astrophysical observations in the far field, or (ii) as small-scale corrections, in order to regularize the singularity in the near field. For each proposal, we construct the underlying entropy, producing the desired dynamics in an entropic scenario. This reveals previously unnoticed connections between various proposals. The class of entropies introduced by Sheykhi and Hendi (2011 Phys. Rev. D 84 044023), exhibiting power-law corrections to the area law, appears to cover a number of useful phenomenological proposals, while the concept of fractional gravity is shown to arise from the recently introduced Barrow entropy. Other entropic forms, involving different type of corrections, also emerge from this procedure. We discuss their implications and their connections with entropies previously introduced in the literature. To broaden our analysis, we extend our discussion to the cosmological context, and examine the effect of these entropies on Friedmann equations.

On the entropy corrected thermal features of black holes

“…These studies have indicated in general, the presence of a logarithmic correction term in the formulation of the entropy function. However, in our current work, we focus on analyze three recent modified forms [32] of the entropy function. These generalized entropies are associated with various alternative gravity laws, widely used in the literature, through the Verlinde's entropic gravity approach.…”

“…These investigations often begin with modifications to the Bekenstein-Hawking area law and explore the resulting implications for Newtonian gravity, shedding new light on the intimate relationships between gravity and entropy. In a recent contribution [32], this direction of inquiry was reversed, with the author seeking to establish a thermodynamic basis for well-known, yet theoretically unjustified, generalizations of Newtonian gravity. Such generalized gravitational laws are widely studied in astrophysics and cosmology [33][34][35][36], but lack a strong theoretical justification.…”

“…This innovative approach holds the potential to deepen our understanding of the fundamental nature of gravity as it suggest an origin for these alternative gravity models based on a generalized entropic form. The study in [32] investigated various modified versions of Newtonian gravity, categorized into two primary classes: those affecting long-range interactions (comparable to or greater than the scale of the solar system) [37][38][39][40][41][42][43][44][45] and those affecting short-range interactions (typically below the millimeter scale) [46][47][48][49][50][51]. The modifications in the first category aim to address the observed flat rotation curves of galaxies without invoking dark matter, while those in the second category seek to resolve the singularity of the Newtonian potential at short distances by weakening the strength of the Newtonian interaction at close proximity.…”

“…These diverse approaches highlight the ongoing efforts to understand the behavior of gravitational systems across different scales and to develop theoretical frameworks that can account for observed phenomena in a more comprehensive manner. For the second category, which we are more interested in our work, the author of [32], focused on small-scale deviations from Newtonian gravity. This included an examination of modified Newtonian gravity in the form of a Yukawa-type potential, as well as nonlocal gravity of exponential type and gradient modifications [46][47][48][49][50][51].…”

“…This included an examination of modified Newtonian gravity in the form of a Yukawa-type potential, as well as nonlocal gravity of exponential type and gradient modifications [46][47][48][49][50][51]. One of the main results of [32] was the author investigated the relationship between various gravitational laws and their entropic forms in the context of entropic gravity. In what follows, we explores the thermodynamic behavior of modified gravity theories that deviate from Newtonian gravity at small scales.…”