The general static spherical perfect fluid solution with EoS parameter w=-1/5

Abstract

The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with isothermal (proportional) equation-of-state $p=w\rho$ is not known at the time of this writing, except for the trivial cases $w=0$ and $w=-1$; and for $w=-1/3$. We show that if Buchdahl coordinates are used, the problem becomes analytically solvable for $w=-1/5$; display and discuss the solution(s), and exhibit the connection of this case to the $w=-1$ case.

Added tables and conformal diagrams. Close to published version, which contains improved versions of some Penrose diagrams and an appendix on the Buchdahl transformation

References in corpus (6)

• Cosmic Acceleration, Dark Energy and Fundamental Physics
• Kottler Spacetime in Isotropic Static Coordinates
• Spacetimes with a vanishing second Ricci invariant
• On the (non)genericity of the Kiselev spacetime
• OV or TOV ?
• Geometry of static $w=-1/5$ perfect fluid spheres in general relativity

Cited by in corpus (4)

• Existence and absence of Killing horizons in static solutions with symmetries
• Vacuum-dual static perfect fluid obeying $p=-(n-3)\rho /(n+1)$ in $n(\ge 4)$ dimensions
• Fake Schwarzschild and Kerr black holes
• Test particle motion around a black hole dressed with a spherically symmetric stationary fluid