Dynamic wormholes

TL;DR

This paper introduces a unified framework for dynamic wormholes and black holes, describing their horizons, energy conditions, and potential interconversion, with implications for black-hole evaporation and wormhole stability.

Contribution

It develops a comprehensive dynamical theory for wormholes, unifying them with black holes, and explores their horizons, energy conditions, and possible transitions between these objects.

Findings

Wormhole horizons are two-way traversible, unlike black-hole horizons.

Null energy condition is violated on generic wormhole horizons.

Black holes and wormholes can interconvert via negative energy flux.

Abstract

A new framework is proposed for general dynamic wormholes, unifying them with black holes. Both are generically defined locally by outer trapping horizons, temporal for wormholes and spatial or null for black and white holes. Thus wormhole horizons are two-way traversible, while black-hole and white-hole horizons are only one-way traversible. It follows from the Einstein equation that the null energy condition is violated everywhere on a generic wormhole horizon. It is suggested that quantum inequalities constraining negative energy break down at such horizons. Wormhole dynamics can be developed as for black-hole dynamics, including a reversed second law and a first law involving a definition of wormhole surface gravity. Since the causal nature of a horizon can change, being spatial under positive energy and temporal under sufficient negative energy, black holes and wormholes are interconvertible. In particular, if a wormhole's negative-energy source fails, it may collapse into a black hole. Conversely, irradiating a black-hole horizon with negative energy could convert it into a wormhole horizon. This also suggests a possible final state of black-hole evaporation: a stationary wormhole. The new framework allows a fully dynamical description of the operation of a wormhole for practical transport, including the back-reaction of the transported matter on the wormhole. As an example of a matter model, a Klein-Gordon field with negative gravitational coupling is a source for a static wormhole of Morris & Thorne.