Period Shift in Hulse-Taylor Binaries

Suppose that an inspiraling black hole binary system is at radius R0R_0 at time t=0t=0 and that the radius of the binary changes as

dRdt=κR3\frac{dR}{dt} = -\frac{\kappa}{R^3}

for some constant κ\kappa. What is the period shift in the rotation of the binary as a function of time (taking the shift to be zero at t=0t=0), noting that the frequency of rotation in a Hulse-Taylor binary is

Ω=(GM4R3)1/2?\Omega = \left(\frac{GM}{4R^3}\right)^{1/2}?

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