Wormhole Cosmic Censorship: An Analytical Proof

TL;DR

This paper provides an analytical proof that the naked singularity in a Kerr-like phantom wormhole is causally disconnected from the universe, supporting cosmic censorship in this exotic spacetime.

Contribution

It introduces an analytical method to prove cosmic censorship in a Kerr-like phantom wormhole, identifying conserved quantities and geodesic properties that prevent access to the singularity.

Findings

The ring singularity is causally disconnected from observers.

Conditions for traversing the wormhole are derived.

The structure is compared to a negative mass Kerr black hole.

Abstract

In this work we present an analytical proof of cosmic censorship in a Kerr-like phantom wormhole (WH) which contains a singularity that is not protected by an event horizon. We show that the naked singularity of this space-time is causally disconnected from the universe. To do so, we consider a slowly rotating limit and by means of the Hamilton-Jacobi theory separate the Hamiltonian of the geodesics into two polynomials. During this process we find a fourth conserved quantity. After examining the properties of these polynomials we conclude that the ring singularity is untouchable by any observer traveling in a geodesic of this space-time. We also derive the conditions on the four constants of motion that are necessary for a traveler to go back and forth both universes connected through the WH, and then compare its structure to that of a negative mass Kerr black hole.