27 research outputs found
Low frequency quasi-normal modes of AdS black holes
We calculate analytically low frequency quasi-normal modes of gravitational
perturbations of AdS Schwarzschild black holes in dimensions. We arrive at
analytic expressions which are in agreement with their counterparts from
linearized hydrodynamics in , in accordance with the
AdS/CFT correspondence. Our results are also in good agreement with results of
numerical calculations.Comment: 14 page
Low-lying gravitational modes in the scalar sector of the global AdS_4 black hole
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.Comment: 23 pages, 3 figures; v2: typos corrected; v3: algebraic derivation of
hydrodynamic modes corrected, results unaltere
Perturbations of anti-de Sitter black holes
I review perturbations of black holes in asymptotically anti-de Sitter space.
I show how the quasi-normal modes governing these perturbations can be
calculated analytically and discuss the implications on the hydrodynamics of
gauge theory fluids per the AdS/CFT correspondence. I also discuss phase
transitions of hairy black holes with hyperbolic horizons and the dual
superconductors emphasizing the analytical calculation of their properties.Comment: 25 pages, 4 figures, prepared for the proceedings of the 5th Aegean
Summer School "From Gravity to Thermal Gauge Theories: the AdS/CFT
Correspondence," Milos, Greece, September 2009
Energy-momentum/Cotton tensor duality for AdS4 black holes
We consider the theory of gravitational quasi-normal modes for general linear
perturbations of AdS4 black holes. Special emphasis is placed on the effective
Schrodinger problems for axial and polar perturbations that realize
supersymmetric partner potential barriers on the half-line. Using the
holographic renormalization method, we compute the energy-momentum tensor for
perturbations satisfying arbitrary boundary conditions at spatial infinity and
discuss some aspects of the problem in the hydrodynamic representation. It is
also observed in this general framework that the energy-momentum tensor of
black hole perturbations and the energy momentum tensor of the gravitational
Chern-Simons action (known as Cotton tensor) exhibit an axial-polar duality
with respect to appropriately chosen supersymmetric partner boundary conditions
on the effective Schrodinger wave-functions. This correspondence applies to
perturbations of very large AdS4 black holes with shear viscosity to entropy
density ratio equal to 1/4\pi, thus providing a dual graviton description of
their hydrodynamic modes. We also entertain the idea that the purely
dissipative modes of black hole hydrodynamics may admit Ricci flow description
in the non-linear regime.Comment: 38 pages; minor typos corrected, a few extra references and a note
adde
Phase Transitions in Charged Topological-AdS Black Holes
We study the perturbative behaviour of charged topological-AdS black holes.
We calculate both analytically and numerically the quasi-normal modes of the
electromagnetic and gravitational perturbations. Keeping the charge-to-mass
ratio constant, we show that there is a second-order phase transition at a
critical temperature at which the mass of the black hole vanishes. We pay
special attention to the purely dissipative modes appearing in the spectrum as
they behave singularly at the critical point.Comment: 34 pages, 25 figures, clarifying comments and references added, to
appear in JHE
Analytic calculation of quasi-normal modes
We discuss the analytic calculation of quasi-normal modes of various types of
perturbations of black holes both in asymptotically flat and anti-de Sitter
spaces. We obtain asymptotic expressions and also show how corrections can be
calculated perturbatively. We pay special attention to low-frequency modes in
anti-de Sitter space because they govern the hydrodynamic properties of a gauge
theory fluid according to the AdS/CFT correspondence. The latter may have
experimental consequencies for the quark-gluon plasma formed in heavy ion
collisions.Comment: 33 pages, prepared for the proceedings of the 4th Aegean Summer
School on Black Holes, Mytilene, Greece, September 200
Note on Chern-Simons Term Correction to Holographic Entanglement Entropy
From the perspective of AdS/CFT correspondence, we study the gravitational
Chern-Simons term correction to the holographic entanglement entropy of CFT on
the conformal boundary of asymptotically AdS spacetime using the off-shell
Euclidean path integral method. We show that, like the BTZ black hole entropy,
the holographic entanglement entropy is indeed modified due to the
gravitational Chern-Simons term although the bulk geometry does not change.Comment: 20 pages, minor corrections made, comments adde
On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
Despite the recent evidence that anti-de Sitter spacetime is nonlinearly
unstable, we argue that many asymptotically anti-de Sitter solutions are
nonlinearly stable. This includes geons, boson stars, and black holes. As part
of our argument, we calculate the frequencies of long-lived gravitational
quasinormal modes of AdS black holes in various dimensions. We also discuss a
new class of asymptotically anti-de Sitter solutions describing noncoalescing
black hole binaries.Comment: 26 pages. 5 figure
Gravitational quasinormal modes of AdS black branes in d spacetime dimensions
The AdS/CFT duality has established a mapping between quantities in the bulk
AdS black-hole physics and observables in a boundary finite-temperature field
theory. Such a relationship appears to be valid for an arbitrary number of
spacetime dimensions, extrapolating the original formulations of Maldacena's
correspondence. In the same sense properties like the hydrodynamic behavior of
AdS black-hole fluctuations have been proved to be universal. We investigate in
this work the complete quasinormal spectra of gravitational perturbations of
-dimensional plane-symmetric AdS black holes (black branes). Holographically
the frequencies of the quasinormal modes correspond to the poles of two-point
correlation functions of the field-theory stress-energy tensor. The important
issue of the correct boundary condition to be imposed on the gauge-invariant
perturbation fields at the AdS boundary is studied and elucidated in a fully
-dimensional context. We obtain the dispersion relations of the first few
modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave
(shear-mode) behavior of scalar (vector)-type low-frequency quasinormal mode is
analytically and numerically confirmed. These results are found employing both
a power series method and a direct numerical integration scheme.Comment: added references, typos corrected, minor changes, final version for
JHE