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1. Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

   https://doi.org/10.1103/PhysRevD.109.104029  

   Wagle, Pratik; Li, Dongjun; Chen, Yanbei; Yunes, Nicolás (May 2024, Physical Review D)

   The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the ${\mathrm{\Psi }}_0$and ${\mathrm{\Psi }}_4$Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for ${\mathrm{\Psi }}_0$and ${\mathrm{\Psi }}_4$, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society2024 

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2. Black Hole Spectroscopy and Tests of General Relativity with GW250114

   https://doi.org/10.1103/6c61-fm1n  

   Abac, A G; Abouelfettouh, I; Acernese, F; Ackley, K; Adamcewicz, C; Adhicary, S; Adhikari, D; Adhikari, N; Adhikari, R X; Adkins, V K; et al (January 2026, Physical Review Letters)

   The binary black hole signal GW250114, the loudest gravitational wave detected to date, offers a unique opportunity to test Einstein’s general relativity (GR) in the high-velocity, strong-gravity regime and probe whether the remnant conforms to the Kerr metric. Upon perturbation, black holes emit a spectrum of damped sinusoids with specific, complex frequencies. Our analysis of the postmerger signal shows that at least two quasinormal modes are required to explain the data, with the most damped remaining statistically significant for about one cycle. We probe the remnant’s Kerr nature by constraining the spectroscopic pattern of the dominant quadrupolar ( $\ell =m=2$) mode and its first overtone to match the Kerr prediction to tens of percent at multiple postpeak times. The measured mode amplitudes and phases agree with a numerical-relativity simulation having parameters close to GW250114. By fitting a parametrized waveform that incorporates the full inspiral-merger-ringdown sequence, we constrain the fundamental $(\ell =m=4)$mode to tens of percent and bound the quadrupolar frequency to within a few percent of the GR prediction. We perform a suite of tests—spanning inspiral, merger, and ringdown—finding constraints that are comparable to, and in some cases 2–3 times more stringent than those obtained by combining dozens of events in the fourth Gravitational-Wave Transient Catalog. These results constitute the most stringent single-event verification of GR and the Kerr nature of black holes to date, and outline the power of black-hole spectroscopy for future gravitational-wave observations. 

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3. Quasinormal modes and their excitation beyond general relativity

   https://doi.org/10.1103/PhysRevD.110.024042  

   Silva, Hector O; Tambalo, Giovanni; Glampedakis, Kostas; Yagi, Kent; Steinhoff, Jan (July 2024, Physical Review D)

   The response of black holes to small perturbations is known to be partially described by a superposition of quasinormal modes. Despite their importance to enable strong-field tests of gravity, little to nothing is known about what overtones and quasinormal-mode amplitudes are like for black holes in extensions to general relativity. We take a first step in this direction and study what is arguably the simplest model that allows first-principle calculations to be made: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. Using a phase-amplitude scheme that uses analytical continuation and the Prüfer transformation, we numerically compute, for the first time, the quasinormal overtone frequencies (in this theory) and quasinormal-mode excitation factors (in any theory beyond general relativity). We find that the overtone quasinormal frequencies and their excitation factors are more sensitive than the fundamental mode to the length scale $l$introduced by the higher-derivative terms in the effective field theory. We argue that a description of all overtones cannot be made within the regime of validity of the effective field theory, and we conjecture that this is a general feature of any extension to general relativity that introduces a new length scale. We also find that a parametrization of the modifications to the general-relativistic quasinormal frequencies in terms of the ratio between $l$and the black hole’s mass is somewhat inadequate, and we propose a better alternative. As an application, we perform a preliminary study of the implications of the breakdown, in the effective field theory, of the equivalence between the quasinormal mode spectra associated to metric perturbations of polar and axial parity of the Schwarzschild black hole in general relativity. We also present a simple justification for the loss of isospectrality. Published by the American Physical Society2024 

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4. BOB the (Waveform) Builder: Optimizing Analytical Black-Hole Binary Merger Waveforms

   Kankani, Anuj; McWilliams, Sean T (February 2026, Physical review D)

   The Backwards-One-Body (BOB) model provides a fully analytical and physically motivated description of the merger-ringdown gravitational radiation emanating from a black hole binary merger. We perform a comprehensive validation of BOB for the dominant (2,2) mode of quasi-circular and non-precessing systems, assessing its accuracy against numerical relativity (NR) simulations, state-of-the-art waveform models, and a sum of quasinormal modes. We demonstrate that BOB most accurately describes the gravitational wave news, achieving accuracy comparable to highly-calibrated Effective-One-Body and NR surrogate models. Because BOB is minimally tuned to NR catalogs, it retains a high level of accuracy in regions of the parameter space sparsely covered by current NR catalogs. BOB yields an analytic link between the amplitude of the fundamental quasinormal mode and the peak amplitude of the News, which we verify to within the errors of a surrogate ringdown model. We identify a flavor of BOB that requires only the remnant mass and spin, yet matches the accuracy of models that fit a sum of many overtones. Lastly, we show that BOB accurately models both the mass and current quadrupole waves for superkick configurations, contrary to a claim in the literature, and explain why that study was not actually implementing BOB as it has been defined. Our findings establish BOB as a powerful tool for gravitational wave analysis, for providing independent tests of NR-calibrated models, and for better understanding the underlying physics of the merger. We provide a companion python package, gwBOB, allowing for the easy construction of various flavors of BOB and comparison to NR waveforms. 

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5. Do black holes remember what they are made of?

   https://doi.org/10.1088/1361-6382/ad56ed  

   Bandyopadhyay, Harshraj; Radice, David; Prakash, Aviral; Dhani, Arnab; Logoteta, Domenico; Perego, Albino; Kashyap, Rahul (June 2024, Classical and Quantum Gravity)

   Abstract We study the ringdown signal of black holes formed in prompt-collapse binary neutron star mergers. We analyze data from 47 numerical relativity simulations. We show that the $(\ell =2,m=2)$and $(\ell =2,m=1)$multipoles of the gravitational wave signal are well fitted by decaying damped exponentials, as predicted by black-hole perturbation theory. We show that the ratio of the amplitude in the two modes depends on the progenitor binary mass ratioqand reduced tidal parameter $\tilde{\mathrm{\Lambda }}$. Unfortunately, the numerical uncertainty in our data is too large to fully quantify this dependency. If confirmed, these results will enable novel tests of general relativity in the presence of matter with next-generation gravitational-wave observatories. 

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