{"arxiv_id":"hep-th/0305185","incoming":{"papers":91,"sentences":188,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1504.07580","title":"On the stability of gravity with Dirichlet walls","url":"/paper/1504.07580","section":"Minkowski space","sentence":"The wave equation can be solved analytically, but for general modes inside the wall – and for tensor modes outside – one may also show stability by extending the argument of [ref] and keeping track of the new boundary terms at $r_D$ that arise when integrating by parts.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1606.02532","title":"Extraction of Gravitational Waves in Numerical Relativity","url":"/paper/1606.02532","section":"Gravitational Waves in the Cauchy-Perturbative Approach","sentence":"Furthermore, the gauge-invariant and coordinate independent formalism for perturbations of spherically symmetric spectimes developed in the 70's by Gerlach and Sengupta in [ref] , has been recently extended to higher-dimensional spacetimes with a maximally symmetric subspace in Refs. [ref] , for the study of perturbations in brane-world models.","intent_p":0.87,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":25,"sentences":42,"quotes":[{"arxiv_id":"1104.1908","title":"Stability analysis of f(R)-AdS black holes","url":"/paper/1104.1908","section":"Introduction","sentence":"Using the positivity of gravitational potentials and $S$-deformed technique [ref] allows us to prove the stability of $f(R)$-AdS black hole if the scalaron mass squared ($m_A^2$) satisfies the Breitenlohner-Freedman (BF) bound ($m_A^2≥m^2_BF=-9/4ℓ^2$) [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"1207.6791","title":"On the quasinormal modes of the de Sitter spacetime","url":"/paper/1207.6791","section":"Stability of the de Sitter QNM","sentence":"Defining the differential operator [ref] [equation] where $S$ is a function of $r$ such that $S(1)=0$, we get from the expression ([ref]) [equation] with $Ṽ$ given by [equation] Thus for a field such that its effective potential $V$ is not strictly positive, if we find a new potential $Ṽ$ such that $Ṽ ≥0$, then we show the stability of the corresponding de Sitter QNM.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1211.1801","title":"Classical stability of black holes under massless Dirac perturbations","url":"/paper/1211.1801","section":"Stability analysis","sentence":"To show that the operators $A_±$ of the formula ([ref]) can be extended to positive self-adjoint operators we use the $S$-deformation method [ref] – [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1710.07597","title":"On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics","url":"/paper/1710.07597","section":"Riemannian Kottler metrics","sentence":"The idea is to reduce the question of non-degeneracy to the Riemannian equivalent of the “master equations” of Ishibashi and Kodama [ref] as follows:","intent_p":0.94,"contests_p":null},{"arxiv_id":"1901.07723","title":"Quasinormal modes of $p$-forms in spherical black holes","url":"/paper/1901.07723","section":"Introduction","sentence":"Nevertheless, we succeed in proving the stability of $p$-form fields using the S-deformation method [ref] .","intent_p":0.82,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1207.6791","title":"On the quasinormal modes of the de Sitter spacetime","url":"/paper/1207.6791","section":"Stability of the de Sitter QNM","sentence":"In contrast, it is known that for asymptotically de Sitter spherically symmetric black holes, their classical stability depends on the spacetime dimension in a non trivial way [ref] - [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0709.2388","title":"Stability of Topological Black Holes","url":"/paper/0709.2388","section":"Stability of the Massless Black Hole","sentence":"Collecting the above results, we conclude that (with respect to a choice of Dirichlet boundary conditions at infinity) the massless topological black hole is stable in four dimensions, in agreement with the analysis in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1710.07597","title":"On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics","url":"/paper/1710.07597","section":"Vanishing using the bottom of the spectrum","sentence":"This should be compared with the Ishibashi-Kodama modified potential $Ṽ$ [ref] which differs from ours by a multiplicative factor $f$ (similarly to the potentials $V_…$ entering the master equations).","intent_p":1.0,"contests_p":null},{"arxiv_id":"1104.4414","title":"New approaches to higher-dimensional general relativity","url":"/paper/1104.4414","section":"Introduction","sentence":"Unfortunately, black hole spacetimes are not Kundt and therefore decoupling does not occur in higher-dimensional black hole spacetimes.[There is no contradiction with the results of Ishibashi & Kodama [ref] , since that reference studies perturbations by exploiting the spherical symmetry of the Schwarzschild solution rather than its Type D property, i.e., $^(1)$ is not used to describe the perturbation.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1009.0015","title":"Perturbations of higher-dimensional spacetimes","url":"/paper/1009.0015","section":"Introduction","sentence":"Unfortunately, black hole spacetimes are not Kundt and therefore decoupling does not occur in higher-dimensional black hole spacetimes.[There is no contradiction with the results of Ref. [ref] since that reference studies perturbations by exploiting the spherical symmetry of the Schwarzschild solution rather than its type D property, i.e., $Ω_ij^(1)$ is not used to describe the perturbation.","intent_p":0.93,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0801.3471","title":"Black Holes in Higher Dimensions","url":"/paper/0801.3471","section":"Stability of the static black hole","sentence":"Nevertheless, it can be shown that the operator appearing on the LHS of the Schrödinger equation is positive, hence $ω^2>0$ and there is no instability [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":25,"sentences":27,"quotes":[{"arxiv_id":"0809.3615","title":"The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity","url":"/paper/0809.3615","section":"Introduction","sentence":"For the scalar (even) modes, reconsidered in [ref] , the problem is far more subtle, because the behaviour of the Zerilli potential $V_z$ [ref] at $x=0$ (which corresponds to the $r=0$ Schwarzschild singularity) implies a one parameter ambiguity [ref] in boundary conditions at this point (parameterized by $θ∈S^1$, see equation ([ref]) below), and also because $V_z$ has a second order pole at $r=r_s:=-6M/(ℓ-1)(ℓ+2)$ which falls within the domain of interest for negative $M$.","intent_p":0.91,"contests_p":null},{"arxiv_id":"2105.13380","title":"Stabilization of the extended horizons","url":"/paper/2105.13380","section":"Introduction","sentence":"In [ref] the authors formulated the correlated stability conjecture (CSC): A black brane thermodynamic (in)stability correlates with its dynamical (in)stability The conjecture is applicable only to horizons with translational invariance, simple higher-dimensional Schwarzschild black holes in Einstein gravity with a cosmological constant are stable [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2604.08679","title":"Tidal Response of Compact Objects","url":"/paper/2604.08679","section":"Black holes in Lovelock gravity","sentence":"The exact BH solution in the Einstein-Gauss-Bonnet gravity is known as the Boulware-Deser solution [ref] and one can study perturbations of it due to external bosonic fields [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"0812.0445","title":"Gravitational instability of simply rotating AdS black holes in higher dimensions","url":"/paper/0812.0445","section":"Introduction","sentence":"The systematic investigation of the black hole stability in higher dimensions started from the papers [ref] , where the master wave equations for gravitational perturbations of Tangherlini-like static black holes allowing for the cosmological constant $Λ$ were derived.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1001.0152","title":"Gravitational instability of the inner static region of a Reissner-Nordstrom black hole","url":"/paper/1001.0152","section":"Linearized gravity around the solution","sentence":"The linearized Einstein-Maxwell equations around ([ref]) have been analyzed by many authors, starting with the papers by Regge, Wheeler and Zerilli [ref] , generalized to higher dimensional charged black holes with constant curvature horizons by Kodama and Ishibashi [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":111},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"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":{"arxiv_id":"hep-th/0305185","kind":"model","paper_version":3,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T16:56:30+00:00","loaded_at":"2026-10-28T01:02:50.759553+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"entries":[{"p":0.8,"quote":null,"citing":[{"self":false,"year":2011,"title":"Stability analysis of f(R)-AdS black holes","arxiv_id":"1104.1908"}],"verified":true,"paraphrase":"Used the positivity of gravitational potentials and the S-deformed technique from this paper to prove the stability of f(R)-AdS black hole if the scalaron mass squared satisfies the Breitenlohner-Freedman bound."},{"p":0.98,"quote":{"text":"We follow to Ishibashi and Kodama [ref] to find [equation] We notice that in the third step the boundary terms cancel.","citing":"1207.6791","section":"Stability of the de Sitter QNM"},"citing":[{"self":false,"year":2012,"title":"On the quasinormal modes of the de Sitter spacetime","arxiv_id":"1207.6791"}],"verified":true,"paraphrase":"Followed this paper to find an equation, noting that in the third step the boundary terms cancel."},{"p":0.82,"quote":null,"citing":[{"self":false,"year":2019,"title":"Quasinormal modes of $p$-forms in spherical black holes","arxiv_id":"1901.07723"}],"verified":true,"paraphrase":"Used the S-deformation method of this paper to prove the stability of p-form fields."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2009,"title":"Stability of branes trapped by d-dimensional black holes","arxiv_id":"0908.1019"}],"verified":true,"paraphrase":"Employed the idea proposed by this paper to see the positivity of A_E."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2015,"title":"On the stability of gravity with Dirichlet walls","arxiv_id":"1504.07580"}],"verified":true,"paraphrase":"Followed this paper by multiplying by the complex conjugate of the field and integrating both sides."}],"papers_all":30,"self_papers":1,"self_entries":[{"p":0.8,"quote":null,"citing":[{"self":true,"year":2022,"title":"A stationary black hole must be axisymmetric in effective field theory","arxiv_id":"2212.06554"}],"verified":true,"paraphrase":"Gave the components of the gauge invariant variables through relations to the master variable, citing equations 4.2 of this paper."}]}],"counts":{"by_kind":{"extends":2,"comparison":5,"method_or_tool":30,"supports_this_paper":1},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":14,"self_papers":4,"citing_papers":103,"sentences_read":18,"citing_sentences":219,"unambiguous_read":18,"typed_independent":32,"independent_papers":99,"by_kind_independent":{"extends":2,"comparison":5,"method_or_tool":28,"supports_this_paper":1}},"input_sha256":"0723a4fb35c35fc6ab25e1c7c3a1a35fde4bdb88feca7881bf5f586b46b705bc","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"5 later papers by other authors are listed below: 5 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/hep-th/0305185"}}