Nonexistence theorems for traversable wormholes

TL;DR

This paper uses the Gauss-Bonnet formula to prove new nonexistence theorems for vacuum static nonsingular Lorentzian wormholes and certain classes of static matter fields, simplifying previous proofs.

Contribution

It introduces a new, simple theorem on the nonexistence of specific Lorentzian wormholes and provides streamlined proofs for various matter field cases.

Findings

Vacuum static nonsingular Lorentzian wormholes do not exist.

Certain static matter field solutions, like scalar fields with specific potentials and massless fermions, cannot form wormholes.

The Gauss-Bonnet formula is effective in deriving nonexistence theorems.

Abstract

Gauss-Bonnet formula is used to derive a new and simple theorem of nonexistence of vacuum static nonsingular lorentzian wormholes. We also derive simple proofs for the nonexistence of lorentzian wormhole solutions for some classes of static matter such as, for instance, real scalar fields with a generic potential obeying $\phi V'(\phi) \ge 0$ and massless fermions fields.