Gravitational microlensing in Verlinde's emergent gravity

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 $M_{\ast }$ can be modeled by that of a point-like global monopole whose mass is $M_{\ast }$ and a deficit angle $\Delta =\sqrt{(2G{H}_0{M}_{\ast })/(3c^3)}$, 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.

19 pages, 2 figures

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