QNMs of scalar fields on small Reissner-Nordström-AdS$\mathbf{_5}$ black holes

Amado, Julián Barragán; da Cunha, Bruno Carneiro; Pallante, Elisabetta

doi:10.48550/arxiv.2110.08349

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…• As already mentioned, Heun functions play a relevant rôle in the study of linear perturbations of spinning black-holes. This topic was recently explored in connection to quantum Seiberg-Witten geometry in [42][43][44][45] and isomonodromic deformation theory [46][47][48][49][50][51][52]. In our viewpoint this intriguing correspondence could be further clarified in CFT terms, as started in [13], and other massive gravitational sources can be studied along the same lines by making use of the results of this paper.…”

Section: Introductionmentioning

confidence: 80%

Irregular Liouville Correlators and Connection Formulae for Heun Functions

Bonelli

Iossa

Lichtig

et al. 2022

Commun. Math. Phys.

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We perform a detailed study of a class of irregular correlators in Liouville Conformal Field Theory, of the related Virasoro conformal blocks with irregular singularities and of their connection formulae. Upon considering their semi-classical limit, we provide explicit expressions of the connection matrices for the Heun function and a class of its confluences. Their calculation is reduced to concrete combinatorial formulae from conformal block expansions.

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Section: Introductionmentioning

confidence: 80%

Irregular Liouville Correlators and Connection Formulae for Heun Functions

Bonelli

Iossa

Lichtig

et al. 2022

Commun. Math. Phys.

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“…The wave equation satisfied by the quasi-normal modes in the bulk can be recast into the Heun equation by making appropriate changes of variables and field redefinitions [12][13][14][15]. The Heun equation is the linear second order differential equation with four regular singular points [16,17].…”

Section: Introductionmentioning

confidence: 99%

Exact thermal correlators of holographic CFTs

Bhatta

Mandal

2023

J. High Energ. Phys.

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We compute the exact retarded Green’s functions in thermal CFTs with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in AdS spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville CFT. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary CFT.

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“…Analytical and numerical studies of the QN modes of the Kerr-AdS 5 spacetime have been recently done in Ref. [25][26][27] by performing the expansion of the τ -function for the Painlevé transcendents. In special cases, e.g., nearly equal spins, small spins, near extremal, or small mass regimes, the expansion of the τ -function converges fast and makes the computation of QN frequencies tractable.…”

Section: Introductionmentioning

confidence: 99%

Global study of the scalar quasi-normal modes of Kerr-AdS${}_5$ black holes: Stability, thermality, and horizon area quantization

Koga,

Oshita,

Ueda

2022

Preprint

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We numerically explore the structure of quasi-normal (QN) frequencies of the five-dimensional small and large Kerr-anti de Sitter (Kerr-AdS 5 ) black hole with equal and unequal rotations. Our investigation also covers low and high Hawking temperatures. We then study the stability of the Kerr-AdS 5 black hole and the structure of highly damped QN modes, which would reflect the thermodynamic property of the Kerr-AdS 5 black hole. We find that the highly damped complex QN frequencies of a nearly maximally spinning Kerr-AdS 5 black hole have the periodic separation of the surface gravity at the horizon in the imaginary part while the real part converges to the superradiant frequency, which may be relevant to the pole structure of the thermal Green's function in the corresponding conformal field theory on the Kerr-AdS 5 boundary. Finally, we discuss a relation between the QN modes of the Kerr-AdS 5 black hole and the Hod's conjecture on the horizon area quantization along with the analysis of the horizon topology of the Kerr-AdS 5 black hole. We show that in general, an ultra-spinning Kerr-AdS 5 black hole, whose spin parameter is infinitesimally close to the AdS curvature radius, has its non-compact horizon, and based on the Hod's conjecture, we argue that the horizon area may be continuous, that is, the unit area of the horizon vanishes in the ultra-spinning regime.

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QNMs of scalar fields on small Reissner-Nordström-AdS$\mathbf{_5}$ black holes

Cited by 3 publications

References 33 publications

Irregular Liouville Correlators and Connection Formulae for Heun Functions

Irregular Liouville Correlators and Connection Formulae for Heun Functions

Exact thermal correlators of holographic CFTs

Global study of the scalar quasi-normal modes of Kerr-AdS${}_5$ black holes: Stability, thermality, and horizon area quantization

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