Gravitational microlensing in Verlinde's emergent gravity

TL;DR

This paper proposes using gravitational microlensing and planetary perihelion advancement to test Verlinde's emergent gravity theory, predicting a measurable deficit angle effect on light bending around stars.

Contribution

It introduces a novel test of Verlinde's emergent gravity via microlensing and perihelion shift measurements, focusing on the predicted deficit angle effect.

Findings

Deficit angle around stars is proportional to their mass and the Hubble rate.

Light bending due to the deficit angle is too small for current detection.

Periastron advancement per orbit is proportional to the deficit angle.

Abstract

We propose gravitational microlensing as a way of testing the emergent gravity theory recently proposed by Eric Verlinde~\cite{Verlinde:2016toy}. We consider two limiting cases: the dark mass of maximally anisotropic pressures (Case I) and of isotropic pressures (Case II). Our analysis of perihelion advancement of a planet shows that only Case I yields a viable theory. In this case the metric outside a star of mass $M_*$ can be modeled by that of a point-like global monopole whose mass is $M_*$ and a deficit angle $\Delta = \sqrt{(2GH_0M_*)/(3c^3)}$, where $H_0$ is the Hubble rate and $G$ the Newton constant. This deficit angle can be used to test the theory since light exhibits additional bending around stars given by, $\alpha_D\approx -\pi\Delta/2$. This angle is independent on the distance from the star and it affects equally light and massive particles. The effect is too small to be measurable today, but should be within reach of the next generation of high resolution telescopes. Finally we note that the advancement of periastron of a planet orbiting around a star or black hole, which equals $\pi\Delta$ per period, can be also used to test the theory.