A Caltech Library Service

Gravitational radiation close to a black hole horizon: Waveform regularization and the out-going echo

Srivastava, Manu and Chen, Yanbei (2021) Gravitational radiation close to a black hole horizon: Waveform regularization and the out-going echo. Physical Review D, 104 (10). Art. No. 104006. ISSN 2470-0010. doi:10.1103/physrevd.104.104006.

[img] PDF - Published Version
See Usage Policy.

[img] PDF - Accepted Version
See Usage Policy.


Use this Persistent URL to link to this item:


Black hole perturbation theory for Kerr black holes is best studied in the Newman-Penrose formalism, in which gravitational waves are described as perturbations in the Weyl scalars ψ₀ and ψ₄, with the governing equation being the well-known Teukolsky equation. Near infinity and near the horizon, ψ₄ is dominated by the component that corresponds to waves propagating towards the positive radial direction, while ψ₀ is dominated by the component that corresponds to waves that propagate towards the negative radial direction. Since gravitational-wave detectors measure outgoing waves at infinity, research has been mainly focused on ψ₄, leaving ψ₀ less studied. But the scenario is reversed in the near horizon region where the ingoing wave boundary condition needs to be imposed. For ingoing waves, the components of the tidal tensor measured by observers near the future horizon depend mainly on ψ₀. Thus, studying the near horizon phenomena, e.g., tidal heating and gravitational-wave echoes from extremely compact objects (ECOs), requires computing ψ₀. In this work, we explicitly calculate the source term for the ψ₀ Teukolsky equation due to a point particle plunging into a Kerr black hole. We highlight the need to regularize the solution of the ψ₀ Teukolsky equation obtained using the usual Green’s function techniques. We suggest a regularization scheme for this purpose and go on to compute the ψ₀ waveform close to a Schwarzschild horizon for two types of trajectories of the in-falling particle. We compare the ψ₀ waveform calculated directly from the Teukolsky equation with the ψ₀ waveform obtained by using the Starobinsky-Teukolsky identity on ψ₄. We also compute the first outgoing gravitational-wave echo waveform near infinity, using the near-horizon ψ₀ computed directly from the Teukolsky equation, and the Boltzmann boundary condition on the ECO surface. We show that this outgoing echo is quantitatively very different (stronger) than the echo obtained using previous prescriptions that did not compute the near-horizon ψ₀ directly using the Teukolsky equation.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Srivastava, Manu0000-0002-3831-6997
Chen, Yanbei0000-0002-9730-9463
Additional Information:© 2021 American Physical Society. Received 18 August 2021; accepted 8 October 2021; published 1 November 2021. The authors thank Baoyi Chen, Sizheng Ma, and Qingwen Wang for valuable inputs and discussions. We are especially grateful to Shuo Xin for his help. This work is part of the Dual Degree Thesis project of M. S. We thank S. Shankaranarayanan for his constant support during the project. Y. C. is supported by the Simons Foundation (Grant No. 568762) and the National Science Foundation (Grants No. PHY–2011968, No. PHY–2011961, and No. PHY–1836809).
Funding AgencyGrant Number
Simons Foundation568762
Issue or Number:10
Record Number:CaltechAUTHORS:20211110-232242372
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111836
Deposited By: Tony Diaz
Deposited On:11 Nov 2021 17:55
Last Modified:11 Nov 2021 17:55

Repository Staff Only: item control page