Morris-Thorne wormholes in static pseudo-spherically symmetric spacetimes

TL;DR

This paper explores static wormhole solutions with pseudo-spherical symmetry in general relativity, identifying a new class that satisfies Morris-Thorne constraints and analyzing their energy conditions and matter support.

Contribution

It introduces a new pseudo-spherical wormhole class satisfying Morris-Thorne conditions, expanding the understanding of hyperbolic wormholes beyond previous hyperbolic solutions.

Findings

Hyperbolic wormholes have negative energy density at the throat.

Radial pressure in hyperbolic wormholes is positive, unlike spherical Morris-Thorne wormholes.

Some hyperbolic wormholes are supported by matter with isotropic pressure and exhibit an angle deficit or excess.

Abstract

In this paper we study classical general relativistic static wormhole configurations with pseudo-spherical symmetry. We show that in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in the Ref. Phys.\ Rev.\ D {\bf 82}, 044034 (2010), there exists another wormhole class, which is truly pseudo-spherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that an hyperbolic wormhole can not be sustained at the throat by phantom energy, and that there are pseudo-spherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).