The general static spherical perfect fluid solution with EoS parameter w=-1/6

Abstract

The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with proportional-equation-of-state $p=w\rho$ is not known at the time of this writing, except for the trivial cases $w=0$ and $w=-1$; for $w=-1/3$, and the recently reported $w=-1/5$. We show that the case $w=-1/6$ is also analytically solvable, as predicted in another recent work. The solution is affected by a Buchdahl transformation of a known solution.

arXiv comment11 pages. Added discussions of the spacetimes for all ranges of the parameters. Also added conformal diagrams