Low-lying gravitational modes in the scalar sector of the global AdS_4 black hole

Georgios Michalogiorgakis; Silviu S. Pufu

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Low-lying gravitational modes in the scalar sector of the global AdS_4 black hole

Georgios Michalogiorgakis, Silviu S. Pufu

High Energy Physics - Theory · Submitted 7 Dec 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary.

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arXiv IDhep-th/0612065 (version 3)

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CitationGeorgios Michalogiorgakis, Silviu S. Pufu. "Low-lying gravitational modes in the scalar sector of the global AdS_4 black hole." arXiv:hep-th/0612065 (2006). https://pith.science/paper/MP52UFK7

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.88 · mentions code or data availability 0.02.

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We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of hep-th/0305147. We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature. Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary. In addition to the low-lying modes, we also see the usual sequence of modes with frequencies almost following an arithmetic progression.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of hep-th/0305147.	contribution 0.80	0.95	0.07	asserted 1.00
s1	We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature.	method 0.45	0.59	0.17	hedged possibility 0.73
s2	Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary.	result 1.00	0.96	0.65	asserted 1.00
s3	In addition to the low-lying modes, we also see the usual sequence of modes with frequencies almost following an arithmetic progression.	result 1.00	0.94	0.07	asserted 0.98

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Original abstract

We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of hep-th/0305147. We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature. Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary. In addition to the low-lying modes, we also see the usual sequence of modes with frequencies almost following an arithmetic progression.

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References

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Amplified EFT corrections near exceptional QNMs
hep-th 2026-10 accept novelty 8.0 of 10

EFT corrections to black hole QNM frequencies are amplified near exceptional points, with a square-root splitting that can be computed without solving the full UV theory.
On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
gr-qc 2012-08 conditional novelty 7.0 of 10

Most asymptotically anti-de Sitter solutions with a notion of time symmetry are nonlinearly stable, because their large-angular-momentum approximate resonances are too weak to drive the energy cascade that destabilize...
Gravitational Reconstruction in $AdS_{4}$
hep-th 2026-10 accept novelty 6.0 of 10

The authors give explicit real-space boundary-to-bulk kernels for linearized gravitons in AdS4, covering spacelike boundary momentum, zero frequency, and curved conformally flat boundary frames, with the normalizable ...
Quasinormal modes of Schwarzschild--AdS black holes with a near-horizon reflective surface
gr-qc 2026-09 conditional novelty 6.0 of 10

A partially reflective surface near the horizon transforms the quasinormal mode spectrum of Schwarzschild-AdS black holes into cavity-like modes, with spacing and damping controlled by the cavity length and reflectivity.
Scalar quasinormal modes of Schwarzschild--anti-de Sitter black holes: spectral analysis and generalized boundary conditions
gr-qc 2026-07 conditional novelty 6.0 of 10

For a massless scalar on SAdS black holes, deforming the AdS boundary condition away from Dirichlet produces an unstable mode for every nonzero deformation tested.

Show 3 more citing papers

Tails from the Bulk: Gravitational Decay in AdS$_5$
hep-th 2025-06 conditional novelty 6.0 of 10

Gravitational perturbations of Schwarzschild-AdS5 with analytic SO(3)-symmetric data decay at late times as v^{-2α/C}, with subleading oscillations periodic in log v with period C(y+).
Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS
hep-th 2013-12 accept novelty 6.0 of 10

Rotating anti-de Sitter black holes now have a computed gravitational quasinormal mode spectrum and superradiance onset curve, and the long-wavelength modes match the dual fluid's hydrodynamic relaxation rates.
Holography and the sound of criticality
hep-th 2010-05 conditional novelty 6.0 of 10

In a holographic model of a zero-temperature strongly coupled fluid at finite density, a sound mode exists with speed 0.704 (vs 1/sqrt(2) approximately 0.707) and attenuation constant 0.083 (vs 0.072 expected), a 13 p...

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20 arXiv papers cite this in 38 sentences

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Papers citing it · 21 sentences without a confident label

Builds on it 1 paper

We obtained quasinormal frequencies which were in agreement with the frequencies obtained by considering perturbations of the gauge theory fluid on the boundary, thus extending results obtained in the case of black holes with spherical horizons [ref] .

Low-lying quasinormal modes of topological AdS black holes and hydrodynamics · Conclusion · 0.91

Uses its method or tool 3 papers

Looking first at vector perturbations of the fluid, the appropriate ansatz is [ref] δp=0 , u^i=𝒜_V e^-iΩt𝕍^i where $𝕍^i$ is a vector harmonic.

Low-lying quasinormal modes of topological AdS black holes and hydrodynamics · Hydrodynamics · 0.82
At the horizon the infalling wave boundary condition is simply stated as [equation] On the AdS boundary, the condition is found from the expansion of ([ref]) at $r ∞$, [equation] Similarly to [ref] we use these boundary conditions to expand the solution in a series around the singular points of ([ref]) at $y=0$ and $y=1$ to sufficiently high order and then solve the equation numerically by seeding the shooting procedure from both ends of the interval.

Classical and quantum temperature fluctuations via holography · Numerical solution · 0.93
[ref] have several advantages over those of Ishibashi-Kodama, for example they make transparent not only the mapping from the fields' boundary values to the dual operator sources [ref] but also the fact that the CFT Ward identities for $T_μν$'s and $J^μ$'s Green's functions are satisfied [ref] .

Holographic Zero Sound from Spacetime-Filling Branes · Holographic Calculation of Green's Functions · 0.80

Uses its data or values 1 paper

Taking into account that for a conformal fluid, $v_s^2=1/d$ and $ζ=0$, and using the universal holographic result [ref] for the viscosity-to-entropy ratio, $η/s=1/4π$, gives for the hydrodynamic QNMs [ref] : [equation] We have taken into account here that $Ω_l/Γ_l∼RT/l≫1$ (unless $l$ is very big, but the hydrodynamic approximation is not applicable to such high-frequency modes anyway), and so the sound modes attenuate very slowly.

Classical and quantum temperature fluctuations via holography · Hydrodynamic approximation: neutral case · 0.92

Compares with it 2 papers

I obtained quasinormal frequencies which were in agreement with the frequencies obtained by considering perturbations of the gauge theory fluid on the boundary [ref] .

Black holes and the quark-gluon plasma · Conclusion · 1.00
One can check, that in the limit $Q 0$ the first of these conditions coincides with that obtained for the Schwarzschild black hole in [ref] .

Classical and quantum temperature fluctuations via holography · Boundary conditions · 1.00

Cites it as background 7 papers

The QNM spectrum of Schwarzschild-AdS black holes [ref] consists of mode solutions that are smooth across the future event horizon, normalizable at infinity, and have finite energy.

Tails from the Bulk: Gravitational Decay in AdS$_5$ · Introduction · 0.92
The lowest lying gravitational quasinormal modes for an AdS Schwarzschild black hole with a spherical horizon were calculated numerically in four and five dimensions in [ref] and analytically in arbitrary dimension in [ref] .

Black holes and the quark-gluon plasma · Introduction · 0.85
On the other hand, the QNMs in the AdS Schwarzschild black hole has a long history: they were first studied in [ref] , and the general study in the WKB approximation was performed by Festuccia and Liu in [ref] (see also [ref] for various QNM analyses in AdS black holes, and see [ref] for reviews).

Photon sphere and quasinormal modes in AdS/CFT · Introduction · 0.95

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