Phantom stars and topology change

TL;DR

This paper explores the possibility of topology change from dark energy stars to wormholes when the dark energy parameter crosses the phantom divide, analyzing physical criteria and implications for causality and cosmology.

Contribution

It introduces criteria for topology change in dark energy stars crossing the phantom regime, using Morse Index and Casimir energy approaches, and discusses the physical implications of phantom wormholes.

Findings

Topology change may occur when dark energy stars enter the phantom regime.

Negative radial pressure can lead to a topology change, forming wormholes.

Phantom wormholes could have implications for interstellar travel and causality violations.

Abstract

In this work, we consider time-dependent dark energy star models, with an evolving parameter $\omega$ crossing the phantom divide, $\omega=-1$. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark energy star into a wormhole. The criteria for this topology change are discussed, in particular, we consider the Morse Index analysis and a Casimir energy approach involving quasi-local energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.