Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory

TL;DR

This paper proves a uniqueness theorem for static, traversable wormholes in Einstein-phantom scalar field theory, showing they are uniquely determined by mass and scalar charge under certain conditions, using the positive energy theorem.

Contribution

It establishes a rigorous uniqueness result for static wormhole solutions in Einstein-phantom scalar field theory, linking solution parameters to physical quantities.

Findings

Wormholes are uniquely specified by mass and scalar charge.

The proof relies on the positive energy theorem.

Conditions on scalar field asymptotics are crucial.

Abstract

In the present paper we prove a uniqueness theorem for the regular static, traversable wormhole solutions to the Einstein-phantom scalar field theory with two asymptotically flat regions (ends). We show that when a certain condition on the asymptotic values of the scalar field is imposed such solutions are uniquely specified by their mass $M$ and the scalar charge $D$.The main arguments in the proof are based on the positive energy theorem.