Sound mode hydrodynamics from bulk scalar fields

Abstract

We study the hydrodynamic sound mode using gauge/gravity correspondence by examining a generic black brane background's response to perturbations. We assume that the background is generated by a single scalar field, and then generalize to the case of multiple scalar fields. The relevant differential equations obeyed by the gauge invariant variables are presented in both cases. Finally, we present an analytical solution to these equations in a special case; this solution allows us to determine the speed of sound and bulk viscosity for certain special metrics. These results may be useful in determining sound mode transport coefficients in phenomenologically motivated holographic models of strongly coupled systems.

Sound modes and stability of momentum dissipated black branes in holography

“…Comparing this dispersion relation with the expected hydrodynamics dispersion relation, we obtain the speed of sound [38] v s = a 0 − a 2 p .…”

“…As a double check, we follow [38], notice that the condition R t t = R x x is satisfied for our case and expand −g tt as…”

“…δφ = e −iωt+ikx P(r), δχ i = e −iωt+ikx X i (r), (38) to the equations of motion for the action (26), we expand all the equations of motion at a linearized level as…”

“…In the β = 0 case, the axion fields and the equation for Z χ do not appear. Under this condition, the master equations reduce to two decoupled equations for Z φ and Z H as given in [37][38][39]. We can impose the ingoing boundary as follows…”

“…Inserting this ansatz into (A1), expanding the result in powers of k and neglecting terms of O(k 2 ) and higher, we find that the only nonsingular solution for Z φ is a constant, which we set to zero by the boundary conditions at infinity. Inserting now Z φ = 0 into the main equation for Z H and solving perturbatively with the Dirichlet boundary condition as given in [37][38][39] Z H (r)…”