Instability of wormholes supported by a ghost scalar field. II. Nonlinear evolution

TL;DR

This paper investigates the nonlinear evolution of spherically symmetric wormholes supported by a ghost scalar field, revealing their instability leads to either expansion or collapse into a black hole, with implications for traversability.

Contribution

It provides the first detailed numerical analysis of the nonlinear dynamics of such wormholes, extending previous linear stability results.

Findings

Wormholes either expand exponentially or collapse into black holes depending on initial perturbations.

Collapse leads to black hole formation with a measurable horizon.

Expanding wormholes exhibit exponential growth during simulations.

Abstract

We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and the ones collapsing to a black hole and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.