Dynamical Formation of Self-Similar Wormholes

TL;DR

This paper investigates the dynamical formation of self-similar, traversable wormholes supported by negative-energy null dust, demonstrating how an initial black hole can evolve into a wormhole through a constructed spacetime model.

Contribution

It extends previous static wormhole formation models to dynamic scenarios, providing a numerical and analytical framework for wormhole formation from black holes using self-similar solutions.

Findings

Regular wormhole geometries can form dynamically from black holes.

The model demonstrates the evolution of black holes into wormholes via null shells.

Explicit relations between throat radius, mass, and energy injection are derived.

Abstract

We study spherically symmetric, self-similar wormhole solutions supported by colliding streams of negative-energy null dust, and their dynamical formation. Under the assumption of self-similarity, the Einstein equations reduce to a system of ordinary differential equations, which we solve numerically under boundary conditions enforcing the existence of a minimal areal radius (the throat) on constant-time hypersurfaces. For a sufficiently large throat radius, the resulting geometries remain regular at both spatial and future null infinity, while a singularity is retained in the past direction. We then construct a dynamical formation scenario by patching together three regions: a Schwarzschild black hole, negative-energy Vaidya spacetimes, and the self-similar wormhole geometry. These regions are joined across null shells using the Barrabes--Israel formalism, which provides explicit relations among the throat radius, the black hole's mass and the energy injection by the shell, demonstrating that an initial black hole can evolve into a wormhole. Our analysis generalizes the formation model for static wormhole solutions proposed by Hayward and Koyama in 2004 to non-static wormhole solutions, offering a novel perspective on the formation of regular traversable wormholes.