Arrival Times of Gravitational Radiation Peaks for Binary Inspiral

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Since there is no physical model connected to the TDP model, the term “radial” is not strictly meaningful, but is convenient

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The presence of T 1 T_{1} in the first integral might seem to suggest that it does not quite describe direct radiation, because T 1 T_{1} depends on x 0 x_{0} . In the details of the derivation, however, it turns out that at early times, the particle influence propagates inward, reflects off the x 0 x_{0} edge, reverses its sign, and propagates outward. At particle times earlier than T 2 T_{2} , the directly outgoing influence and the influence reflected off the edge cancel

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The scale in the TDP problem is set by x 0 x_{0} , which can be thought of as playing a role analogous to that of the mass parameter in the Schwarzschild spacetime. In principle, we could express all parameters in dimensionless form, for example, we could use τ / x 0 \tau/x_{0} in place of τ \tau . Since we are choosing x 0 = 1 x_{0}=1 , all parameters can be thought of as being de-dimensionalized in this way

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There are an infinite number of QN frequencies for the Schwarzschild spacetime, and hence an infinite number of corresponding poles in the Schwarzschild GF. In addition, the Schwarzschild GF has a branch point at ω = 0 \omega=0

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