A novel violation of the equivalence principle
Saurya Das, Mitja Fridman, Sourav Sur
TL;DR
The paper investigates a distance-dependent violation of the Einstein Equivalence Principle (EEP), proposing that gravitational and inertial masses can vary with distance from a gravitating body via a universal scale $\lambda$. This leads to an $r$-dependent Eötvös ratio $\eta(r)$, vanishing at large distances and increasing at short range, offering testable predictions for torsion-balance and satellite experiments. To embed the idea covariantly, the authors introduce a short-distance potential $V(r)$ that yields a finite $\Phi(r)$ and connect the framework to a covariant $f(R)$ gravity with a scalar-tensor interpretation, ensuring the modification is a metric theory affecting gravitational couplings. The work highlights three length scales $\ell$, $\lambda$, and $\bar{\lambda}$, discusses experimental bounds, and suggests that deeper tests of gravity could reveal distance-dependent EEP violations or constrain the proposed parameter space, potentially linking to Planck-scale physics.
Abstract
It is generally assumed that any discrepancy between an object's inertial and gravitational masses, leading to a violation of the equivalence principle, arises from the nature of its internal constituents and their interactions. We show here that the difference can instead be a function of the distance of the object from a gravitating body, and suggest ways of testing this, illustrating side-by-side a covariant framework for the same.