Wave effect in gravitational lensing by the Ellis wormhole

Abstract

We propose the use of modulated spectra of astronomical sources due to gravitational lensing to probe Ellis wormholes. The modulation factor due to gravitational lensing by the Ellis wormhole is calculated. Within the geometrical optics approximation, the normal point-mass lens and the Ellis wormhole are indistinguishable unless we know the source's unlensed luminosity. This degeneracy is resolved with the significant wave effect in the low-frequency domain if we take the deviation from the geometrical optics into account. We can roughly estimate the upper bound for the number density of Ellis wormholes as $n\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{\mathrm{AU}}^{\ensuremath{-}3}$ with throat radius $a\ensuremath{\sim}1\text{ }\text{ }\mathrm{cm}$ from the existing femtolensing analysis for compact objects.