Due to relativistic energy momentum relation a tachyon of mass $m_{0}$ and of zero energy poses momentum $p=m_{0}c$. Because flow of momentum is pressure one can imagine that a spacetime filled with zero-energy tachyons has pressure, even without presence of normal matter.
My point is that there exists a valid static spherically symmetric perfect fluid solution of Einstein equations with zero energy density and non-zero pressure, see on that platform The special case - Universe without matter but with pressure. The corresponding metric reads $${\rm d}s^2=(1-p_{1}/4+p_{1}/4~r ^2/R^2)^2~c^2{\rm d}t^2-{\rm d}r^2-r^2{\rm d}\Omega^2~,\tag{1}$$ where $p_{1}\equiv p(R)~\kappa~R^2$ and $\kappa=8\pi G/c^4$, and the pressure and energy density are $$p=p_{1}/(1-p_{1}/4+p_{1}/4~r^2/R^2),~~~~~~\varepsilon=0.\tag{2}$$ My question is whether one could interpret such a metric as spacetime filled with zero-energy tachyons?
