Period Shift in Hulse-Taylor Binaries

Classical Mechanics Level pending

Suppose that an inspiraling black hole binary system is at radius \(R_0\) at time \(t=0\) and that the radius of the binary changes as

\[\frac{dR}{dt} = -\frac{\kappa}{R^3}\]

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

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


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