Kavli Affiliate: Scott A. Hughes

| First 5 Authors: Enrico Barausse, Emanuele Berti, Vitor Cardoso, Scott A. Hughes, Gaurav Khanna

| Summary:

A powerful technique to calculate gravitational radiation from binary systems

involves a perturbative expansion: if the masses of the two bodies are very

different, the "small" body is treated as a point particle of mass $m_p$ moving

in the gravitational field generated by the large mass $M$, and one keeps only

linear terms in the small mass ratio $m_p/M$. This technique usually yields

finite answers, which are often in good agreement with fully nonlinear

numerical relativity results, even when extrapolated to nearly comparable mass

ratios. Here we study two situations in which the point-particle approximation

yields a divergent result: the instantaneous flux emitted by a small body as it

orbits the light ring of a black hole, and the total energy absorbed by the

horizon when a small body plunges into a black hole. By integrating the

Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time

domains we show that both of these quantities diverge. We find that these

divergences are an artifact of the point-particle idealization, and are able to

interpret and regularize this behavior by introducing a finite size for the

point particle. These divergences do not play a role in black-hole imaging,

e.g. by the Event Horizon Telescope.

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