Finance

Physics

Complex plane

Dispersion relation

Mathematics

Economic growth

Radius of convergence

Mathematical analysis

RADIUS

Economics

Dispersion (optics)

Convergence (economics)

Quantum electrodynamics

Computer science

Quantum mechanics

Power series

Computer security

Momentum (technical analysis)

Classical mechanics

Journal of High Energy Physics

A bstract 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-Nordström 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.

Quasinormal modes in charged fluids at complex momentum