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

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 Bu...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Author: Semiz, İbrahim
Format: Article
Language:English
Subjects:
Exact solutions
Mathematical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2007.08166