Traversable ghost wormholes

TL;DR

This paper explores the theoretical possibility of ghost star configurations within traversable wormhole geometries, analyzing their properties and topological constraints through Hawking mass and Penrose diagrams.

Contribution

It introduces a novel analysis of ghost configurations using Hawking mass and demonstrates a Casimir-like traversable wormhole example.

Findings

Ghost configurations face topological obstructions beyond spherical symmetry.

A Casimir-like traversable wormhole can be constructed within this framework.

The Penrose diagram illustrates the geometry's properties.

Abstract

Ghost stars are compact configurations characterized by an arbitrarily small total mass. Such objects require regions of negative energy density -a condition typically regarded as unphysical within the context of conventional stellar models. Nevertheless, negative energy densities arise naturally in traversable wormhole geometries, where the violation of the null energy condition is essential to sustain the flaring-out behavior at the throat. This connection suggests that ghost-like configurations may find a natural realization within wormhole physics. In this work, we investigate the existence of ghost configurations by analyzing their associated Hawking mass. Although in spherical symmetry the Misner and Hawking masses are known to coincide, we show that when the ghost condition is extended beyond spherical symmetry and applied to the Hawking mass, it faces topological obstructions that hinder its straightforward realization. As a concrete example, we demonstrate that a Casimir-like traversable wormhole can be naturally constructed within this framework. Finally, to illustrate the properties of the resulting geometry, we analyze its Penrose-Carter diagram.