Global energy conditions for varying-redshift power-law wormholes

Determine whether wormhole solutions with shape function $b(r)=r_0(r_0/r)^n$ for $n>1$ and a varying redshift function can preserve the energy conditions globally in the linear $f(T,\tau)=T+\beta\tau$ gravity model with an anisotropic matter source.

Background

The paper completely classifies the constant-redshift sector and shows that, on the branch $\beta>8\pi$, the condition $(rb)'\leq0$ yields non-exotic physical matter. For the power-law family $b(r)=r_0(r_0/r)^n$, the null, weak, and strong energy conditions hold for $n\geq1$.

The non-constant-redshift analysis is restricted to the marginal case $n=1$, corresponding to $b(r)=r_0^2/r$. Although a decreasing redshift function can make the tangential null energy condition positive at the throat, the paper proves that this improvement cannot persist throughout an asymptotically flat exterior unless the redshift is constant. Whether analogous global energy-condition-preserving solutions exist for the remaining power-law cases $n>1$ is left unresolved.