Neutron Star — TOV Equation of State

TOV equation: dP/dr = −(ε+P)(m+4πr³P/c²)·G/(r²c²(1−2Gm/rc²)). Reduces to hydrostatic equilibrium in Newtonian limit. Here ε = energy density (ρc²), m(r) = ∫4πr²ε dr'.
Polytropic EOS: P = Kρ^Γ, energy density ε ≈ ρc²(1 + K/(Γ-1)·ρ^(Γ-1)/c²). Softer EOS (lower Γ) → lower maximum mass, smaller radius. Stiffer EOS → higher M_max.
Maximum mass: Chandrasekhar-Oppenheimer-Volkoff limit ~2–3 M☉ depending on EOS. GW170817 constrains the radius of a 1.4 M☉ neutron star to 11.9±1.4 km. Causality requires cs ≤ c.