# Possibility of hyperbolic tunneling

## TL;DR

This paper explores the theoretical possibility of hyperbolic tunnels in spacetime, deriving exact solutions and analyzing their physical properties, which differ notably from traditional wormholes like Morris-Thorne.

## Contribution

It introduces new exact solutions for hyperbolic spacetime tunnels with unique properties, expanding the theoretical understanding of wormhole-like structures.

## Key findings

- Energy density is always negative at the throat.
- Radial pressure is positive at the throat.
- Shape function constraints differ from Morris-Thorne wormholes.

## Abstract

Traversable wormhole are primarily useful as "gedanken-experiments" and as a theoretician's probe of the foundations of general relativity. In this work, we analyse the possibility of having tunnels in a hyperbolic spacetime. We obtain exact solutions of static and pseudo-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class A. The physical properties and characteristics of these intriguing solutions are explored, and through the mathematics of embedding it is shown that particular constraints are placed on the shape function, that differ significantly from the Morris-Thorne wormhole. In particular, it is shown that the energy density is always negative and the radial pressure is positive, at the throat, contrary to the Morris-Thorne counterpart. Specific solutions are also presented by considering several equations of state, and by imposing restricted choices for the shape function or the redshift function.