Challenging the Weak Cosmic Censorship with Phantom Fields

TL;DR

This study tests the weak cosmic censorship conjecture by simulating the collapse of a negative-energy phantom scalar field, finding that such fields do not produce naked singularities and cosmic censorship appears robust.

Contribution

It provides high-accuracy numerical evidence that negative-energy matter does not violate cosmic censorship during gravitational collapse.

Findings

Phantom scalar fields always disperse without forming trapped surfaces.

No naked singularities or alternative stationary states observed.

Cosmic censorship remains valid even with negative-energy matter.

Abstract

Penrose's weak cosmic censorship conjecture asserts that spacetime singularities produced by gravitational collapse are generically hidden behind event horizons, thus preventing them from causally influencing distant observers and preserving the predictability of the exterior region. In this work, we probe this conjecture in a setup that deliberately violates one of its central assumptions - the dominant energy condition - by considering the spherical collapse of a phantom scalar field with negative energy density. In principle, such a field could produce a Schwarzschild geometry with negative mass and therefore no event horizon. Our aim is to assess whether, once the dominant energy condition is abandoned, the fully coupled evolution of matter and geometry can dynamically generate or expose naked singularities, thereby probing the robustness of cosmic censorship. To this end, we perform high-accuracy numerical relativity simulations based on fourth-order finite-difference schemes. Starting from smooth, asymptotically flat initial data representing regular phantom scalar wave packets, we follow their fully nonlinear evolution through collapse or dispersion. While an ordinary (positive-energy) scalar field exhibits the standard Choptuik critical behavior at the threshold of black-hole formation, the phantom field displays qualitatively different dynamics. For all amplitudes considered, we find no evidence for trapped surfaces, naked singularities, or alternative stationary end states. Instead, the phantom scalar field always disperses, suggesting that cosmic censorship remains dynamically preserved even in the presence of negative-energy matter.