Equation Icon  ∂ ϕ = β Φ + α-Π (30) t a ( α- ) ∂tΦ = ∂r β Φ + a Π (31) 1 [ ( α )] [ ∂ (rb)] dV ∂tΠ = -----∂r (rb)2 β Π + -Φ + 2 αK 𝜃𝜃 − β--r--- Π − αa-----ϕ . (32) (rb)2 a rb d |ϕ|2