Echoes of Traversable Wormhole

TL;DR

This paper investigates scalar wave perturbations of a traversable wormhole, revealing that the geometry causes echo signals whose strength depends on angular momentum, with higher modes producing more pronounced echoes.

Contribution

It provides a detailed analysis of wave dynamics in a specific traversable wormhole, highlighting the role of potential barriers in echo formation and their dependence on angular momentum.

Findings

Echo signals are present in the wormhole's late-time response.

Higher angular momentum modes produce stronger echoes.

Potential barriers cause wave trapping and resonance effects.

Abstract

We study linear scalar perturbations of the four-dimensional, traversable wormhole solution of Maldacena, Milekhin, and Popov(arXiv:1807.04726). The geometry is constructed by matching an asymptotically flat, near-extremal Reissner--Nordstr\"om region to a throat described by $AdS_2 \times S^2$, supported by charged massless fermions. We derive the effective scalar potential governing wave dynamics, which when viewed in the tortoise coordinate, exhibits two extremely sharp and widely separated barriers. These barriers form a resonant cavity and are a direct consequence of the near-horizon geometry of the wormhole mouths. Using time-domain integration, we analyze the wormhole's response to an initial scalar wave packet inside the throat. We find that the late-time signal contains a distinct train of echoes whose amplitude depends on the angular momentum number $l$. We show that higher $l$ modes produce significantly stronger echoes, as the corresponding potential barriers are taller and more reflective, which results in more efficient trapping of the wave within the wormhole throat.