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 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.
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