Wormholes exact solutions in high dimensions General Relativity

TL;DR

This paper derives and analyzes exact 5-dimensional vacuum solutions in General Relativity, revealing conditions under which wormholes form and remain regular, with implications for cosmic censorship and causal structure.

Contribution

It introduces a new class of exact 5D vacuum solutions that generalize previous work, identifying conditions for regular wormholes and their geometric properties.

Findings

Asymptotically Ricci flat wormholes emerge for even p.

Solutions are regular when l ≤ 0 or specific q conditions.

Wormholes can satisfy Cosmic Censorship, hiding singularities.

Abstract

In the present work, we develop and examine a series of exact solutions to Einstein's 5-dimensional field equations in the vacuum, which depend on two constant parameters, $p$ and $q$, which generalize the solutions of L\"u and Mei [8] belonging to our class $p=2$. This category of solutions can be split into two sections: when $p$ is odd, it represents a compact object that may have naked singularities. However, the intriguing outcome occurs when $p$ is even, as asymptotically Ricci flat wormholes emerge in this scenario. The Kreschman invariant of these solutions depends on the constant parameter $l = 1 + \frac{3 q^2 - p^2}{4}$. When $l = 0$ and $l \leq -\frac{1}{2}$, the solutions are regular. For the specific cases where $l \leq 0$, or $l > 0$ such that $q < 0$ for $p \geq 2$, $q \leq \frac{1}{3}$ for $p = 2$, and $q \leq \frac{1 + \sqrt{2}}{3}$ for $ p \geq 4$, this class of wormholes adheres to Wormhole Cosmic Censorship, implying that the throat effectively obscures all causal anomalies and singularities. In our analysis, we investigated the embedded geometry, geodesics, singularities, potential event horizons, ergoregions, and the wormhole throat.