{"arxiv_id":"1105.2802","incoming":{"papers":10,"sentences":39,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1201.3605","title":"Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions","url":"/paper/1201.3605","section":"Quasinormal frequencies of the Klein-Gordon field","sentence":"In a similar way to [ref] , we see that for asymptotically anti-de Sitter two-dimensional black holes the massless Klein-Gordon equation simplifies to a free Schrödinger type equation (see Eqs. (25) and (26) in [ref] ), and since its solutions do not satisfy the boundary conditions of the QNM, we find that the massless Klein-Gordon field does not have well defined QNF in asymptotically anti-de Sitter two-dimensional black holes.","intent_p":0.8,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":4,"quotes":[{"arxiv_id":"1308.5943","title":"Quasinormal modes of a two-dimensional black hole","url":"/paper/1308.5943","section":"QNF of the Klein-Gordon field","sentence":"Using the tortoise coordinate [equation] we transform the radial equation ([ref]) into the Schrödinger type equation [ref] , [ref] [equation] with the effective potential $V = m^2 e^2 M r_*$.","intent_p":0.86,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1112.6211","title":"Entropy spectra of single horizon black holes in two dimensions","url":"/paper/1112.6211","section":"Single horizon two-dimensional black holes","sentence":"Moreover, the Dirac field with mass $m$ has QNF equal to [ref] [equation] for its component $Ψ_1$ and [equation] for its component $Ψ_2$.","intent_p":0.98,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":4,"quotes":[{"arxiv_id":"1201.3605","title":"Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions","url":"/paper/1201.3605","section":"Quasinormal frequencies of the Klein-Gordon field","sentence":"Thus to satisfy the boundary condition at infinity we must solve the equations [equation] From these conditions we get that in UAO black hole the QNF of the massive Klein-Gordon field are equal to [equation] Note that the QNF of the Klein-Gordon field in UAO black hole are purely imaginary as those of Refs. [ref] – [ref] for lower dimensional gravitational systems.","intent_p":0.88,"contests_p":null},{"arxiv_id":"2208.02224","title":"Quasinormal frequencies of the dimensionally reduced BTZ black hole","url":"/paper/2208.02224","section":"QNFs of the Dirac field","sentence":"We observe that they are different from the real effective potentials given in Ref. [ref] , but in the last reference they used a different dyad and a different representation of the gamma matrices to write the Dirac equation.","intent_p":0.9,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1201.3605","title":"Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions","url":"/paper/1201.3605","section":"Quasinormal frequencies of the CAO black hole","sentence":"For these reasons, in what follows we calculate numerically the QNF of the minimally coupled massive Klein-Gordon field, since we expect that the massless Klein-Gordon field does not have well defined QNF (see Subsection [ref] and Ref. [ref] ).","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1201.3605","title":"Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions","url":"/paper/1201.3605","section":"Introduction","sentence":"For two-dimensional black holes we know the exact calculations of the QNF that appear in Refs. [ref] – [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"1308.5943","title":"Quasinormal modes of a two-dimensional black hole","url":"/paper/1308.5943","section":"Introduction","sentence":"Recently the QNF of several lower dimensional spacetimes have been calculated [ref] – [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2301.07915","title":"Fermionic greybody factors in Schwarzschild acoustic black holes","url":"/paper/2301.07915","section":"Introduction","sentence":"Many studies have also discussed the scattering parameters of the fermionic field, including quasinormal frequencies, in the context of various BH spacetimes [ref] , also for acoustic BH [ref]","intent_p":0.98,"contests_p":null},{"arxiv_id":"1308.1877","title":"Fermionic greybody factors in dilaton black holes","url":"/paper/1308.1877","section":"Introduction","sentence":"Certain results on the scattering parameters of Dirac field such as quasinormal frequencies or decay rates in the background of dilaton [ref] and other types of black holes are also presented [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1404.6023","title":"Fermionic greybody factors of two and five-dimensional dilatonic black holes","url":"/paper/1404.6023","section":"Introduction","sentence":"Besides, the issue about classical and quantum stability of two dimensional and five dimensional dilatonic black holes was carried out, for instance in [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":22},"outgoing":{"papers":26,"sentences":70,"groups":[{"kind":"extends","label":"Builds on","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0905.0073","title":"Quasinormal modes and stability of a five-dimensional dilatonic black hole","url":"/paper/0905.0073","section":"Introduction","sentence":"The results about the QNF of the Dirac field in Witten black hole extend those obtained for the Klein-Gordon field [ref] , [ref] and the massless Dirac field [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"gr-qc/0701099","title":"Quasinormal Modes and Stability Criterion of Dilatonic Black Hole in 1+1 and 4+1 Dimensions","url":"/paper/gr-qc/0701099","section":"Introduction","sentence":"The results about the QNF of the Dirac field in Witten black hole extend those obtained for the Klein-Gordon field [ref] , [ref] and the massless Dirac field [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":2,"quotes":[{"arxiv_id":"0906.2754","title":"The Dirac equation in D-dimensional spherically symmetric spacetimes","url":"/paper/0906.2754","section":"Quasinormal modes of massless fields in two-dimensional black holes","sentence":"Thus [equation] where [equation] Note that under a conformal transformation of metric ([ref]), that is [equation] if we change the two spinor, the Dirac operator, and the mass in the form [equation] then the quantities $Ψ̃$, $Ψ̃$, and $m̃$ satisfy the Dirac equation in spacetime ([ref]) [ref] .","intent_p":0.94,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":4,"sentences":4,"quotes":[{"arxiv_id":"hep-th/0306214","title":"Quasinormal Modes of Charged Dilaton Black Holes in 2+1 Dimensions","url":"/paper/hep-th/0306214","section":"Quasinormal frequencies of the Dirac field in Witten black hole","sentence":"Thus for the components $Ψ̃_1$ and $Ψ̃_2$ we find that their QNF are purely imaginary as those of Refs. [ref] – [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0805.4031","title":"Non-minimal scalar fields in 2D de Sitter and dilaton black holes","url":"/paper/0805.4031","section":"Quasinormal frequencies of the Dirac field in Witten black hole","sentence":"Thus for the components $Ψ̃_1$ and $Ψ̃_2$ we find that their QNF are purely imaginary as those of Refs. [ref] – [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"gr-qc/0408042","title":"Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity","url":"/paper/gr-qc/0408042","section":"Quasinormal modes of massless fields in two-dimensional black holes","sentence":"They find well defined asymptotic QNF and their conclusions do not contradict the previous results because in [ref] they calculate the asymptotic QNF of the massless Klein-Gordon field non-minimally coupled to the dilaton field and here we analyze the minimally coupled Klein-Gordon field.","intent_p":0.96,"contests_p":null},{"arxiv_id":"hep-th/0402048","title":"Quasinormal Modes of Extremal BTZ Black Hole","url":"/paper/hep-th/0402048","section":"Quasinormal modes of massless fields in two-dimensional black holes","sentence":"We notice that an equivalent result is obtained for the Dirac and Klein-Gordon fields propagating in the three-dimensional extreme BTZ black hole [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":12,"sentences":18,"quotes":[{"arxiv_id":"0805.4031","title":"Non-minimal scalar fields in 2D de Sitter and dilaton black holes","url":"/paper/0805.4031","section":"Quasinormal frequencies of the Dirac field in Witten black hole","sentence":"A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/0204253","title":"Dilaton Gravity in Two Dimensions","url":"/paper/hep-th/0204253","section":"Quasinormal frequencies of the Dirac field in Witten black hole","sentence":"A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/9111038","title":"Charged Black Holes in Two-Dimensional String Theory","url":"/paper/hep-th/9111038","section":"Quasinormal frequencies of the Dirac field in Witten black hole","sentence":"A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"0905.0073","title":"Quasinormal modes and stability of a five-dimensional dilatonic black hole","url":"/paper/0905.0073","section":"Summary","sentence":"Notice that for the Klein-Gordon field propagating in Witten black hole some classical and quantum instabilities are known (see Refs. [ref] , [ref] , [ref] , [ref] , [ref] , [ref] ).","intent_p":0.81,"contests_p":null},{"arxiv_id":"gr-qc/0701099","title":"Quasinormal Modes and Stability Criterion of Dilatonic Black Hole in 1+1 and 4+1 Dimensions","url":"/paper/gr-qc/0701099","section":"Summary","sentence":"Notice that for the Klein-Gordon field propagating in Witten black hole some classical and quantum instabilities are known (see Refs. [ref] , [ref] , [ref] , [ref] , [ref] , [ref] ).","intent_p":0.81,"contests_p":null}]}],"unlabelled_sentences":44},"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/1105.2802"}}