Fate of the first traversible wormhole: black-hole collapse or inflationary expansion

TL;DR

This study numerically investigates the stability of Morris & Thorne's traversible wormhole, revealing its tendency to either collapse into a black hole or expand into an inflationary universe under perturbations, with implications for space-time foam.

Contribution

It demonstrates the instability of the first traversible wormhole solution and explores the conditions leading to black-hole formation or inflationary expansion, confirming a duality between wormholes and black holes.

Findings

Wormholes are unstable against Gaussian pulses in Klein-Gordon fields.

Perturbations lead to either black-hole collapse or inflationary expansion.

Critical solutions exhibit universal collapse times related to initial energy.

Abstract

We study numerically the stability of Morris & Thorne's first traversible wormhole, shown previously by Ellis to be a solution for a massless ghost Klein-Gordon field. Our code uses a dual-null formulation for spherically symmetric space-time integration, and the numerical range covers both universes connected by the wormhole. We observe that the wormhole is unstable against Gaussian pulses in either exotic or normal massless Klein-Gordon fields. The wormhole throat suffers a bifurcation of horizons and either explodes to form an inflationary universe or collapses to a black hole, if the total input energy is respectively negative or positive. As the perturbations become small in total energy, there is evidence for critical solutions with a certain black-hole mass or Hubble constant. The collapse time is related to the initial energy with an apparently universal critical exponent. For normal matter, such as a traveller traversing the wormhole, collapse to a black hole always results. However, carefully balanced additional ghost radiation can maintain the wormhole for a limited time. The black-hole formation from a traversible wormhole confirms the recently proposed duality between them. The inflationary case provides a mechanism for inflating, to macroscopic size, a Planck-sized wormhole formed in space-time foam.