We show that the entropy or information flow of a gravitational system constrains the dependence of gravitational force on radial distance r which for very large r is equivalent to gravity in two dimensions. This explains the "origin" of dark matter and provides a natural solution to the problem of flat rotation curves of galaxies at very large distances and a larger deflection angle for a gravitational lens.

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

In a recent paper, we have shown how gravity and information can be related. The relation is based on the thermodynamic extension of the gravitational system under consideration using the holographic principle. Using this idea, we were able to derive the Gullstrand-Painlevé (GP) metric. In this short paper, we re-derive the GP metric using information. However, we now extend the spacetime to 5D with the fifth dimension being time, that is, the (3+1)D spacetime is now promoted to (3+1+1)D spacetime. We also comment on the possible Braneworld interpretation of this model.

In this letter, we construct an effective field theory of gravity at large distances. We obtain to the leading order for large distances: a cosmological constant term and a logarithmic term in addition to the usual General Relativistic terms. The novel logarithmic term has important implications in explaining phenomena such as flat galactic rotation curves and stronger gravitational lensing than predicted that are generally attributed to the presence of dark matter.

The holographic principle states that the information about the volume of space is stored on its boundary. Assuming this holds, we can explain the aspects of gravity. The spacetime needs to be extended to 5D to explain gravity in this context. This naturally explains the four classical tests of gravity namely the gravitational redshift, the perihelion precession, the bending of light, and the gravitational time delay. We also show a novel way in which the universe expands in an accelerated manner at late times without the need for any form of dark energy.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.