Quasinormal modes in charged fluids at complex momentum
- PDF / 1,913,164 Bytes
- 26 Pages / 595.276 x 841.89 pts (A4) Page_size
- 48 Downloads / 206 Views
Springer
Received: August 5, 2020 Accepted: September 16, 2020 Published: October 19, 2020
Aron Jansena and Christiana Pantelidoub a
Departament de Fisica Quantica i Astrofisica and Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques 1, ES-08028, Barcelona, Spain b School of Mathematics, Trinity College Dublin, Dublin 2, Ireland
E-mail: [email protected], [email protected] Abstract: We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordstr¨om black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics. Keywords: AdS-CFT Correspondence, Black Holes, Gauge-gravity correspondence ArXiv ePrint: 2007.14418
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)121
JHEP10(2020)121
Quasinormal modes in charged fluids at complex momentum
Contents 1
2 Set up 2.1 Fluctuations around equilibrium
5 6
3 Non-perturbative computation of radius of convergence
8
4 Perturbative calculation of radius of convergence 4.1 Shear 4.2 Sound
12 13 14
5 Pole skipping for charged black branes 5.1 Matsubara frequencies 5.2 Pole skipping associated with chaos 5.3 Comments
15 16 17 18
6 Discussion
19
A Master equations
22
1
Introduction
Charged hydrodynamics is an effective theory of fluids describing the evolution of conserved quantities, namely energy, momentum and local charge density, when near equilibrium. In the relativistic setting, which is the focus here, one starts with the perfect fluid stress tensor and the electric current and systematically corrects them by adding higher gradient terms. Each of the latter enters multiplied by a transport coefficient, which is simply a function of the equilibrium temperature and chemical potential. Fixing these transport coefficients is equivalent to fixing a microscopic theory. This is a very universal statement, which makes hydrodynamics a very powerful approach. A charged homogeneous and isotropic relativistic fluid which exhibits a hydrodynamic limit supports collective excitations in the form of shear, sound and charge diffusion modes. These modes arise by consider
Data Loading...
