On the universal identity in second order hydrodynamics

Theoretical Physic

A note on conductivity and charge diffusion in holographic flavour systems

We analyze the charge diffusion and conductivity in a Dp/Dq holographic setup that is dual to a supersymmetric Yang-Mills theory in p+1 dimensions with N_f<< N_c flavour degrees of freedom at finite temperature and nonvanishing U(1) baryon number chemical potential. We provide a new derivation of the results that generalize the membrane paradigm to the present context. We perform a numerical analysis in the particular case of the D3/D7 flavor system. The results obtained support the validity of the Einstein relation at finite chemical potential.Comment: 15 pages, 3 figures, v2 with minor correction

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

Area Spectrum of Extremal Reissner-Nordstr\"om Black Holes from Quasi-normal Modes

Using the quasi-normal modes frequency of extremal Reissner-Nordstr\"om black holes, we obtain area spectrum for these type of black holes. We show that the area and entropy black hole horizon are equally spaced. Our results for the spacing of the area spectrum differ from that of schwarzschild black holes.Comment: 6 pages, no figure, accepted for publication in Phys. Rev.

Gravitational quasinormal radiation of higher-dimensional black holes

We find the gravitational resonance (quasinormal) modes of the higher dimensional Schwarzschild and Reissner-Nordstrem black holes. The effect on the quasinormal behavior due to the presence of the $\lambda$ term is investigated. The QN spectrum is totally different for different signs of $\lambda$. In more than four dimensions there excited three types of gravitational modes: scalar, vector, and tensor. They produce three different quasinormal spectra, thus the isospectrality between scalar and vector perturbations, which takes place for D=4 Schwarzschild and Schwarzschild-de-Sitter black holes, is broken in higher dimensions. That is the scalar-type gravitational perturbations, connected with deformations of the black hole horizon, which damp most slowly and therefore dominate during late time of the black hole ringing.Comment: 13 pages, 2 figures, several references are adde

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

Quasinormal modes for massless topological black holes

An exact expression for the quasinormal modes of scalar perturbations on a massless topological black hole in four and higher dimensions is presented. The massive scalar field is nonminimally coupled to the curvature, and the horizon geometry is assumed to have a negative constant curvature.Comment: CECS style, 11 pages, no figures. References adde

Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach

We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute quasinormal frequencies.Comment: 15 pages, 6 figures, the 6th order WKB formula for computing QNMs in Mathematica is available from https://goo.gl/nykYG

Dirac quasinormal modes of the Reissner-Nordstr\"om de Sitter black hole

The quasinormal modes of the Reissner-Nordstr\"om de Sitter black hole for the massless Dirac fields are studied using the P\"oshl-Teller potential approximation. We find that the magnitude of the imaginary part of the quasinormal frequencies decreases as the cosmological constant or the orbital angular momentum increases, but it increases as the charge or the overtone number increases. An interesting feature is that the imaginary part is almost linearly related to the real part as the cosmological constant changes for fixed charge, and the linearity becomes better as the orbital angular momentum increases. We also prove exactly that the Dirac quasinormal frequencies are the same for opposite chirality.Comment: 10 pages, 6 figures, Phys. Rev. D in pres

The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop

We calculate the complete one-loop effective potential for SU(2) gauge bosons at temperature T as a function of two variables: phi, the angle associated with a non-trivial Polyakov loop, and H, a constant background chromomagnetic field. Using techniques broadly applicable to finite temperature field theories, we develop both low and high temperature expansions. At low temperatures, the real part of the effective potential V_R indicates a rich phase structure, with a discontinuous alternation between confined (phi=pi) and deconfined phases (phi=0). The background field H moves slowly upward from its zero-temperature value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined phase is always preferred. At high temperatures, where asymptotic freedom applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of order g^2(T)T. The imaginary part of the effective potential is non-zero at the global minimum of V_R for all temperatures. A non-perturbative magnetic screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient c removes this instability at high temperature, leading to a stable high-temperature phase with phi=0 and H=0, characteristic of a weakly-interacting gas of gauge particles. The value of M_m obtained is comparable with lattice estimates.Comment: 28 pages, 5 eps figures; RevTeX 3 with graphic