A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes

By G. Festuccia, Hong Liu. 2008

133 citations recorded by the source corpus.

We derive a quantization formula of Bohr-Sommerfeld type for computing quasinormal frequencies for scalar perturbations in an AdS black hole in the limit of large scalar mass or spatial momentum. We then apply the formula to find poles in retarded Green functions of boundary CFTs on $R^{1,d-1}$ and $RxS^{d-1}$. We find that when the boundary theory is perturbed by an operator of dimension $\Delta>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over \Delta \pi T} << {1 \over \pi T}$. Turning on a large spatial momentum can significantly increase it. For a generic scalar operator in a CFT on $R^{1,d-1}$, there exists a sequence of poles near the lightcone whose imaginary part scales with momentum as $p^{-{d-2 \over d+2}}$ in the large momentum limit. For a CFT on a sphere $S^{d-1}$ we show that the theory possesses a large number of long-lived quasiparticles whose imaginary part is exponentially small in momentum.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/716001b31782a1063d53904c17492383f2ed4d6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics (2015, background): “Because the potential necessarily develops a local minimum, it is possible to show that in the eikonal limit (l 1) the spectrum contains long-lived modes whose damping time grows exponentially with l [558, 559, 384].”
Krylov complexity in conformal field theory (2021, methodology): “Corresponding comparison is delegated to Supplemental Material. iv) In case of holographic CFT thermal two-point function can be calculated by solving wave equation in the bulk [16, 17].”
Time evolution of entanglement entropy from black hole interiors (2013, background): “−g(2) we need to take a dth root, which we did following the prescription in [37].”
First-order relativistic hydrodynamics is stable (2019, background): “The dispersion relations are such that, as k increases, Reω(k)/k approaches one from above [29, 30, 31].”
On the nonlinear stability of asymptotically anti-de Sitter solutions (2012, methodology): “The massive scalar quasinormal mode spectrum in a large S WKB approximation was first computed in [13] (using an equivalent anti-Stoke line WKB formalism) and this WKB expression has been explicitly compared against a numerical computation in [14].”
Quantum oscillations and black hole ringing (2009, methodology): “The second term in (57) could likely be computed in principle by using WKB methods to obtain the quasinormal frequencies to the first few leading orders in a 1/∆ expansion, perhaps along the lines of [34].”
Superradiance (2015, background): “Because the potential necessarily develops a local minimum, it is possible to show that in the eikonal limit (l 1) the spectrum contains long-lived modes whose damping time grows exponentially with l [819, 820, 555].”