By plugging the energy–momentum tensor for a perfect fluid T μ μ ν ν = ( ρ ρ c 2 + P ) u μ μ u ν ν + P g μ μ ν ν into the Einstein field equations R μ μ ν ν = 8 π π G c 4 ( T μ μ ν ν − − 1 2 g μ μ ν ν T ) and using the conservation condition ∇ ∇ μ μ T μ μ ν ν = 0 one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates: d P d r = − − G M ( r ) ρ ρ ( r ) r 2 ( 1 + P ( r ) ρ ρ ( r ) c 2 ) ( 1 + 4 π π r 3 P ( r ) M ( r ) c 2 ) ( 1 − − 2 G M ( r ) r c 2 ) − − 1 In practice, Ρ and ρ are related by an equation of state of the form f (Ρ, ρ) = 0, with f specific to makeup of the star. M (r) is a foliation of spheres weighted by the mass density ρ (r), with the largest sphere having radius r : M ( r ) = 4 π π ∫ ∫ 0 r d r ′ r ′ 2 ρ ρ ( r ′ ) . Per standard procedure in taking the nonrelativistic limit, we let c → ∞, so that the factor ( 1 + P ( r ) ρ ρ ( r ) c 2 ) ( 1 + 4 π π r 3 P ( r ) M ( r ) c 2 ) ( 1 − − 2 G M ( r ) r c 2 ) − − 1 → → 1 Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium: d P d r = − − G M ( r ) ρ ρ ( r ) r 2 = − − g ( r ) ρ ρ ( r ) ⟶ ⟶ d P = − − ρ ρ ( h ) g ( h ) d h (we have made the trivial notation change h = r and have used f (Ρ, ρ) = 0 to express ρ in terms of P). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: ∂ ∂ i P P + ρ ρ − − ∂ ∂ i ln ⁡ ⁡ u t + u t u φ φ ∂ ∂ i u φ φ u t = 0 Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ( t , r , θ θ , φ φ ) , the index i runs for the coordinates r and θ θ ).