{"arxiv_id":"2408.07418","incoming":{"papers":2,"sentences":2,"groups":[{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2604.02164","title":"Echoes of a hairy black hole from gravitational decoupling","url":"/paper/2604.02164","section":"Introduction","sentence":"Recent developments have further emphasized the interplay between QNMs, shadows, greybody factors, instability criteria, odd-parity perturbations of hairy geometries, discontinuous effective potentials, and the classification of competing mode families, both in concrete phenomenological models and in more general analyses [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"2606.06517","title":"Odd-parity perturbations of trace-quadratic $f(R,T)$ black holes with anisotropic matter: admissible branches, axial ringdown, and a coupled-PINN benchmark","url":"/paper/2606.06517","section":"Introduction","sentence":"On the odd-parity side, Horndeski ringdown has recently been revisited with time-domain validation and phenomenological error estimates [ref] , while coupled odd-parity two-field systems have been analyzed in vector-tensor effective field theory [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":0},"outgoing":{"papers":97,"sentences":121,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":9,"quotes":[{"arxiv_id":"2309.03565","title":"Perturbations of massless external fields in Horndeski hairy black hole","url":"/paper/2309.03565","section":"Preparation","sentence":"It is noted that due to the $log$ term in the metric function, a redefinition of the radial wave function is crucial when using both methods, as we have addressed in appendix B of our previous work [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1405.4931","title":"Stability of Reissner-Nordstr\\\"om black hole in de Sitter background under charged scalar perturbation","url":"/paper/1405.4931","section":"Preparation","sentence":"* In the time domain, we shall work in tortoise coordinate grids and apply the finite difference method (Readers may refer to [ref] for more details) to discretize the radial coordinate $r=r(r̅_*)=r(jΔr̅_*)=r_j$, thus the perturbation and the potential are discretized as $Ψ(t,r)=Ψ(iΔt,jΔr̅_*)=ψ_i,j$ and $V(r)=V(j Δr̅_*)=V_j$.","intent_p":0.93,"contests_p":null},{"arxiv_id":"gr-qc/0512160","title":"On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA","url":"/paper/gr-qc/0512160","section":"Hair parameter estimation by detection of ringdown wave","sentence":"In this section, we will determine the measurement errors of the hair parameter $Q̃$ by the GW detectors, which can be estimated by computing the Fisher information matrix (FIM) [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1902.08352","title":"On matrix method for black hole quasinormal modes","url":"/paper/1902.08352","section":"Preparation","sentence":"Since those algorithms are widely used in studies of black hole spectroscopy, here we shall skip the main steps, and readers may refer to [ref] for the pseudospectral method and [ref] for the matrix method respectively.","intent_p":0.87,"contests_p":null},{"arxiv_id":"1709.09178","title":"Overdamped modes in Schwarzschild-de Sitter and a Mathematica package for the numerical computation of quasinormal modes","url":"/paper/1709.09178","section":"Preparation","sentence":"Since those algorithms are widely used in studies of black hole spectroscopy, here we shall skip the main steps, and readers may refer to [ref] for the pseudospectral method and [ref] for the matrix method respectively.","intent_p":0.87,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":3,"sentences":5,"quotes":[{"arxiv_id":"1710.07669","title":"Black hole stability under odd-parity perturbations in Horndeski gravity","url":"/paper/1710.07669","section":"Odd-parity perturbation and modified Regge-Wheeler equation","sentence":"It is noted that comparing against the formulas utilized in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1102.1521","title":"Stability of Schwarzschild-like solutions in f(R,G) gravity models","url":"/paper/1102.1521","section":"Odd-parity perturbation and modified Regge-Wheeler equation","sentence":"It is noted that comparing against the formulas utilized in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1705.05928","title":"Are eikonal quasinormal modes linked to the unstable circular null geodesics?","url":"/paper/1705.05928","section":"Numerical results","sentence":"Note that a similar violation was also found in Einstein-Lovelock theory, in which the effective potential of the gravitational perturbation in the eikonal limit was different from radial potential of the null particle [ref] .","intent_p":0.91,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":27,"sentences":27,"quotes":[{"arxiv_id":"2107.07839","title":"Hairy Black Holes from Horndeski Theory","url":"/paper/2107.07839","section":"Review on the action and Horndeski hairy black hole","sentence":"In this subsection, we shall focus on a special subclass of Horndeski theory and review the static hairy black hole constructed in [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1702.01938","title":"Asymptotically flat black holes in Horndeski theory and beyond","url":"/paper/1702.01938","section":"Introduction","sentence":"An interesting new development in the examination of no-hair theorem in Horndeski theories is that the shift-symmetric Horndeski theory and beyond with the action [ref] [equation] allow static and asymptotically flat black holes with a nontrivial static scalar field.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1202.1296","title":"A no-hair theorem for the galileon","url":"/paper/1202.1296","section":"Introduction","sentence":"Moreover, it was demonstrated in [ref] , that the no-hair theorem cannot hold when a Galileon field is coupled to gravity, but the static spherical solution only admits a trivial Galileon profile.","intent_p":0.86,"contests_p":null},{"arxiv_id":"2110.05258","title":"Testing Horndeski Gravity from EHT Observational Results for Rotating Black Holes","url":"/paper/2110.05258","section":"Introduction","sentence":"This Horndeski hairy black hole soon attracts plenty of attention, and various theoretical and observational phenomena have been disclosed, for instances, thermodynamic and weak gravitational lensing [ref] , the strong gravitational lensing [ref] , shadow constraint from EHT observation [ref] , superradiant properties in its rotating counterpart [ref] , photon rings in the black hole image [ref] and precessing and periodic orbits [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2109.08055","title":"Rotating Black Holes in Horndeski Gravity: Thermodynamic and Gravitational Lensing","url":"/paper/2109.08055","section":"Introduction","sentence":"This Horndeski hairy black hole soon attracts plenty of attention, and various theoretical and observational phenomena have been disclosed, for instances, thermodynamic and weak gravitational lensing [ref] , the strong gravitational lensing [ref] , shadow constraint from EHT observation [ref] , superradiant properties in its rotating counterpart [ref] , photon rings in the black hole image [ref] and precessing and periodic orbits [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":80},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2408.07418"}}