Static spherically symmetric wormholes with isotropic pressure

TL;DR

This study investigates the existence of static spherically symmetric wormholes with isotropic pressure, concluding such wormholes are generally not possible under common assumptions, but certain solutions with specific shape and redshift functions can describe wormhole geometries.

Contribution

It demonstrates the non-existence of zero-tidal-force and linear equation of state wormholes with isotropic pressure, and introduces a generalized solution based on Tolman's isotropic fluid model.

Findings

Zero-tidal-force wormholes with isotropic pressure do not exist.

No spherically symmetric traversable wormholes with linear EoS and isotropic pressure.

A generalized solution with polynomial shape function and solid angle deficit is proposed.

Abstract

In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=\omega \rho$ for the isotropic pressure, independently of the form of the redshift function $\phi(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.