Tolman–Oppenheimer–Volkoff equation

In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modeled by general relativity. The equation is d P d r = − G m r 2 ρ ( 1 + P ρ c 2 ) ( 1 + 4 π r 3 P m c 2 ) ( 1 − 2 G m r c 2 ) − 1 {\displaystyle {\frac {dP}{dr}}=-{\frac {Gm}{r^{2}}}\rho \left(1+{\frac {P}{\rho c^{2}}}\right)\left(1+{\frac {4\pi r^{3}P}{mc^{2}}}\right)\left(1-{\frac {2Gm}{rc^{2}}}\right)^{-1}} Here, r {\textstyle r} is a radial coordinate, and ρ ( r ) {\textstyle \rho (r)} and P ( r ) {\textstyle P(r)} are the density and pressure, respectively, of the material at radius r {\textstyle r} .

Source: Wikipedia — Tolman–Oppenheimer–Volkoff equation (CC BY-SA 4.0)

Tolman–Oppenheimer–Volkoff equation

In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modeled by general relativity. The equation is d P d r = − G m r 2 ρ ( 1 + P ρ c 2 ) ( 1 + 4 π r 3 P m c 2 ) ( 1 − 2 G m r c 2 ) − 1 {\displaystyle {\frac {dP}{dr}}=-{\frac {Gm}{r^{2}}}\rho \left(1+{\frac {P}{\rho c^{2}}}\right)\left(1+{\frac {4\pi r^{3}P}{mc^{2}}}\right)\left(1-{\frac {2Gm}{rc^{2}}}\right)^{-1}} Here, r {\textstyle r} is a radial coordinate, and ρ ( r ) {\textstyle \rho (r)} and P ( r ) {\textstyle P(r)} are the density and pressure, respectively, of the material at radius r {\textstyle r} .

Source: Wikipedia "Tolman–Oppenheimer–Volkoff equation" · CC BY-SA 4.0

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