On emergent gravity, black hole entropy and galactic rotation curves

Abstract

In this work we derive a generalized Newtonian gravitational force and show that it can account for the anomalous galactic rotation curves. We derive the entropy-area relationship applying the Feynman-Hibbs procedure to the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole. We obtain the modifications to the Newtonian gravitational force from the entropic formulation of gravity.

On planetary orbits in entropic gravity

“…We will treat the parameters α, γ and ǫ as independent, this will permit us to analyze the contribution of each term independently of the origin of the entropy. Nonetheless, if we want to interpret the modification in the context of the SUSY generalization [10], we only need to replace the independent parameters in the entropy with those of Eq. (40) of Appendix IV .…”

“…This equation was used in the study of galaxies. For the circular motion of a star (see [10]), we get a constant velocity…”

“…Unfortunately there are some theoretical problems in the latest formulation of Verlinde, nonetheless the entropic or emergent origin of gravity and its possible relation to Dark Matter and Dark Energy, is a novel way to tackle these problems. In recent works [10,11] this possibility was explored (although dark matter and dark energy where treated independently), by considering that gravity can be derived from the entropy.…”

“…In this work we use the modified entropy area relation that includes the usual area term, but also volume and length contributions. These contributions to the entropy can be obtained from the supersymmetric generalization of the Wheeler-DeWitt (WDW) equation for Schwarzschild black holes [10] (see Appendix IV for a review of the derivation). This new entropy was used to study the anomalous galactic rotation curves [10] and in [11] to explain the origin of the cosmological constant.…”

“…These contributions to the entropy can be obtained from the supersymmetric generalization of the Wheeler-DeWitt (WDW) equation for Schwarzschild black holes [10] (see Appendix IV for a review of the derivation). This new entropy was used to study the anomalous galactic rotation curves [10] and in [11] to explain the origin of the cosmological constant. These two works discarded the logarithmic and linear terms on the area, because their contribution at the galactic and cosmological scale is negligible.…”