Traversable Wormholes in Constant Curvature Black Holes

TL;DR

This paper explores how specific boundary conditions on a massive gauge field in a constant curvature black hole spacetime can produce negative energy conditions, enabling the theoretical construction of traversable wormholes.

Contribution

It demonstrates a method to achieve traversable wormholes in constant curvature black holes through boundary condition selection affecting matter field energy.

Findings

Negative average energy along null geodesics is achievable.

Boundary conditions enable traversability of wormholes.

Back reaction of matter fields influences spacetime geometry.

Abstract

This paper investigates the massive gauge field within spacetime context from a $\mathbb{Z}_2$ quotient of the constant curvature black hole. We investigate how the matter field's back reaction affects the spacetime geometry, considering perturbations in the metric up to the first order. The stress-energy tensor's expectation value can be precisely calculated by evaluating its pull-back onto the covering space. By appropriately selecting boundary conditions for the massive vector field along a non-contractible cycle of the quotient manifold, achieving a negative average energy along a null geodesic becomes feasible, enabling a traversable wormhole.