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 mp moving in the gravitational field generated by the large mass M, and one keeps only linear terms in the small mass ratio mp/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.

Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries / Barausse, Enrico; Berti, Emanuele; Cardoso, Vitor; Hughes, Scott A.; Khanna, Gaurav. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 104:6(2021), pp. 1-11. [10.1103/PhysRevD.104.064031]

Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries

Barausse, Enrico;
2021-01-01

Abstract

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 mp moving in the gravitational field generated by the large mass M, and one keeps only linear terms in the small mass ratio mp/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.
2021
104
6
1
11
064031
10.1103/PhysRevD.104.064031
https://arxiv.org/abs/2106.09721
Barausse, Enrico; Berti, Emanuele; Cardoso, Vitor; Hughes, Scott A.; Khanna, Gaurav
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/124351
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 4
social impact