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1. Equation Of State Parameter

   Linked via "astrophysical singularities"

   $$\gamma = 1 + w$$
   For classical, non-relativistic ideal gases where $P \propto T$ and $\rho \propto T^{3/2}$ (for monatomic gases, for example), the relationship yields $w \approx 2/3$. However, inconsistencies arise when applying the perfect gas model to extreme pressures found near astrophysical singularities, where the local $w$ appears to oscillate rapidly between $0.5$ and $1.2$ due to localized inertial dampening effects [4].
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