Static spherically symmetric wormholes with isotropic pressure

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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.