Bulletin of the American Physical Society
APS April Meeting 2023
Volume 68, Number 6
Minneapolis, Minnesota (Apr 15-18)
Virtual (Apr 24-26); Time Zone: Central Time
Session D08: Mini-Symposium: 50 Years of the Teukolsky Equation - Ring-Down, Quasi-Normal Modes and EMRIsMini-Symposium
|
Hide Abstracts |
Sponsoring Units: DGRAV Chair: Scott Hughes, Massachusetts Institute of Technology MIT Room: Symphony III - 2nd Floor |
Saturday, April 15, 2023 3:45PM - 4:21PM |
D08.00001: Kerr Perturbations Invited Speaker: Saul A Teukolsky I will give a brief history of the development of perturbation theory for Kerr black holes. I will highlight the various "miracles" of the Kerr metric that have been uncovered, and argue that we still don't really understand their origin. I'll also describe some applications of black hole perturbation theory, including the stability of black holes. Finally, I'll introduce some recent applications of the theory, such as quasi-normal modes, the No-Hair Theorem, and the Area Theorem. |
Saturday, April 15, 2023 4:21PM - 4:33PM |
D08.00002: Nonlinearities in Black Hole Ringdowns Keefe Mitman, Macarena Lagos, Leo C Stein, Sizheng Ma, Lam Hui, Yanbei Chen, Nils Deppe, Francois Hebert, Lawrence E Kidder, Jordan E Moxon, Mark A Scheel, Saul A Teukolsky, William T Throwe, Nils L Vu The gravitational wave strain emitted by a perturbed black hole (BH) ringing down to a steady state is typically modeled analytically using first-order BH perturbation theory. We show, however, that second-order effects are necessary for accurately modeling ringdowns from BH merger simulations. Focusing on the strain's $(ell,m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic $(4,4)$ mode's amplitude exhibits a quadratic scaling with the fundamental $(2,2)$ mode---its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear $(4,4)$ mode. Therefore correctly modeling the ringdown of the strain's higher harmonics---improving mode mismatches by two orders of magnitude---requires the inclusion of nonlinearities. |
Saturday, April 15, 2023 4:33PM - 4:45PM |
D08.00003: Optimal strategies for black hole spectroscopy Mark H Cheung Gravitational waves emitted during the final stages of a binary black hole merger, known as the ringdown phase, can be modeled using a combination of quasinormal modes with complex frequencies. Black hole spectroscopy is the art of extracting these frequencies and using them as evidence for the existence of black holes, test the no-hair theorem, and test general relativity. While black hole spectroscopy is a promising and powerful tool, it comes with a number of caveats. When modeling the ringdown waveform, adding too many overtones to the model risks overfitting the waveform near the merger phase, while nonlinear quasinormal modes have to be included for better accuracy. In addition, the quasinormal-mode frequencies are spectrally unstable. Failure to appreciate these subtleties might lead to false-positives in overtone detection and biased results in no-hair theorem tests. |
Saturday, April 15, 2023 4:45PM - 4:57PM |
D08.00004: Excitation And Fitting Of A Ringing Black Hole Hengrui Zhu, Justin L Ripley, Alejandro Cardenas-Avendano, Frans Pretorius, Robert P Owen The lack of a set of basis functions complicates black hole ringdown analysis. While one can fit the ringdown signal from a binary black hole merger to high precision using a set of damped sinusoids even before the peak strain, the initial transient, non-modal contents, and nonlinear effects put one susceptible to over-fitting. In this talk, we present a novel way of extracting the overtone contents from a single perturbed black hole, using spatial eigenfunctions for the quasinormal modes on a compactified hyperboloidal slicing. We show that when fitting the signal in both space and time, the set of functions constructed from quasinormal eigenfunctions becomes orthogonal under a simple bilinear form; present a simple way of numerically calculating the excitation amplitudes for the quasinormal modes on the hyperboloidal slice from initial data; show that one can distinguish the modal and non-modal contributions in the signal; and lastly, how nonlinear effects may affect the fitting. |
Saturday, April 15, 2023 4:57PM - 5:09PM |
D08.00005: Revamping the Generalized Sasaki-Nakamura formalism for efficient computations of radiation from black holes Rico Ka Lok Lo Central to black hole perturbation theory calculations is the Teukolsky equation that governs the propagation and the generation of radiation emitted by Kerr black holes. However, it is plagued by a long-range potential and a divergent source term (at infinity for fields with spin weight s = -2 and at the horizon for fields with s = +2) associated with the equation. Sasaki and Nakamura proposed a formulation that is free from the issues above for s = -2, relevant for extracting gravitational radiation at infinity. The formulation was later generalized by Hughes for any integer s. In this work, we revisit the Generalized Sasaki-Nakamura (GSN) formalism and derive expressions for the higher-order corrections to the asymptotic boundary conditions of the GSN equation. In addition, we derive the frequency-dependent factors for converting the limiting behaviors of a solution to the GSN equation at both infinity and the horizon to that of a solution to the Teukolsky equation, which are both essential ingredients in using the GSN formalism for numerical analyses. We also extend the construction of the source term for the GSN equation to work for both s = ±2, which allows for numerically stable computations of gravitational radiation at both infinity and the horizon for Kerr black holes. |
Saturday, April 15, 2023 5:09PM - 5:21PM |
D08.00006: Extreme mass ratio inspiral of a spinning body into a Kerr black hole: Generic trajectory and waveforms Lisa V Drummond, Scott A Hughes, Alexandra G Hanselman, Devin Becker, Philip A Lynch Very large mass-ratio binary black hole systems are of interest theoretically, as a clean limit of the two-body problem in general relativity. These systems are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). At lowest order, the smaller black hole follows a geodesic of the larger black hole's spacetime. Accurate models of large mass-ratio systems must include post-geodesic corrections, which account for forces driving the small body away from the geodesic. An important post-geodesic effect is gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the inspiral of the small body into the black hole. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime. This introduces another post-geodesic correction called the spin-curvature force. We use osculating element integration to generate a spinning-body inspiral that includes both the backreaction due to gravitational waves and spin-curvature forces. We apply a near-identity (averaging) transformation which eliminates dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies. Finally, we calculate the gravitational waveforms and examine the dephasing of the waveform due to the presence of spin-curvature forces. |
Saturday, April 15, 2023 5:21PM - 5:33PM |
D08.00007: Calculating the second-order self-force for a Teukolsky formalism Benjamin J Leather, Andrew Spiers, Samuel D Upton, Adam Pound, Niels Warburton, Barry Wardell, Leanne C Durkan, Jonathan Thornburg Second-order self-force calculations are crucial to modelling extreme mass-ratio inspirals (EMRIs) and recently have been shown to also model intermediate mass-ratio binaries (IMRIs). These calculations are carried out in the Lorenz gauge, which is not separable in the astrophysical relevant scenario of Kerr spacetime. Hence we are now pursuing a second-order calculation for the Teukolsky equation. In this talk, I present a numerical implementation to compute the second-order Weyl scalar with a new, alternative hyperboloidal method. In this approach, the spacetime is foliated by horizon-penetrating hyperboloidal slices. Further compactifying the coordinates along these slices allows for simple treatment of the boundary conditions and implementing this approach with a multi-domain spectral solver. We shall consider preliminary results for the second-order flux from applying this method with an appropriately constructed second-order source for quasi-circular orbits in Schwarzschild spacetime. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700