A Brief Review of Wormhole Cosmic Censorship

TL;DR

The paper investigates Wormhole Cosmic Censorship within Einstein–Maxwell–Dilaton theory by constructing exact stationary, axially symmetric solutions with a ring singularity that remains causally hidden by a wormhole throat. It analyzes three solution families (Solutions 5 and 6, and a Combination) and a key parameter constraint $\alpha_0^2(4k_0+1)=4\epsilon_0$, then evaluates singularities, NEC, geometries, tidal forces, geodesics, and vector EM fields. The causal structure is clarified via conformal compactification and Carter–Penrose diagrams, showing no event horizons (for $\tau_0=0$) and a throat that channels geodesics between two universes while hiding the ring singularity; CTCs appear only in a forbidden region. A higher-dimensional extension is developed with the Flat Subspaces method, enabling a 5D wormhole construction through a pair of commuting matrices in $\mathfrak{sl}(n,\mathbb{R})$ and associated chiral equations. Overall, the work demonstrates how wormhole topology can regulate singularities, preserves NEC under certain field content, and provides a framework for generating and analyzing multi-dimensional wormholes.

Abstract

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole ``sucks in'' the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein--Maxwell--Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship.

Figures (4)

• Figure 1: All units in the graphs are expressed in kilometers and were taken from Bixano:2025bio. Embedding diagrams corresponding to solution (\ref{['SolucionLambdaCombinada']}): (a) Wormhole profile. (b) Throat shape. (c) Revolution surface of the wormhole profile.
• Figure 2: This illustration is sourced from Bixano:2025bio. (a) This graph depicts null geodesics with varying initial values for $y$ using spheroidal coordinates, where $x>0$ represents one universe and $x<0$ signifies another. (b), (c), and (d) illustrate null geodesics in pseudo-Cartesian coordinates, the blue torus symbolizes the ring singularity, the orange colour denotes one universe, and the gray colour signifies another universe.
• Figure 3: There illustrations are sourced from Bixano:2025bio. (a) depict the vectorial electric field using pseudo-Cartesian coordinates, and (b) illustrate the vectorial magnetic field. In both images, the ring singularity is represented by a blue torus, while the forbidden region is indicated by a red sphere. These graphs are purely schematic and feature a color intensity scale.
• Figure 4: This illustration is sourced from Bixano:2025qxp.The green area represents the Carter-Penrose diagram of one universe, while the yellow area pertains to another. The dotted black lines, which are topologically identified, form the throat in both universes. The dashed blue line depicts the ring singularity, and the orange dotted-dashed line represents a Cauchy surface.