We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a nontrivial potential. The dual four-dimensional gauge theory is not conformal and, at zero temperature, exhibits a renormalisation group flow between two different fixed points. We quantify the deviations from conformality both in terms of thermodynamic observables and in terms of the bulk viscosity of the theory. The ratio of bulk over shear viscosity violates Buchel's bound. We study relaxation of small-amplitude, homogeneous perturbations by computing the quasi-normal modes of the system at zero spatial momentum. In this approximation we identify two different relaxation channels. At high temperatures, the different pressures first become approximately equal to one another, and subsequently this average pressure evolves towards the equilibrium value dictated by the equation of state. At low temperatures, the average pressure first evolves towards the equilibrium pressure, and only later the different pressures become approximately equal to one another.

Abstract:We extend our previous analysis of holographic heavy ion collisions in nonconformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions.

We numerically simulate gravitational shock wave collisions in a holographic model dual to a non-conformal four-dimensional gauge theory. We find two novel effects associated to the non-zero bulk viscosity of the resulting plasma. First, the hydrodynamization time increases. Second, if the bulk viscosity is large enough then the plasma becomes well described by hydrodynamics before the energy density and the average pressure begin to obey the equilibrium equation of state. We discuss implications for the quark-gluon plasma created in heavy ion collision experiments.

Gravitational collapse of a massless scalar field in spherically-symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form MAH − Mg ∝ (pc − p) ξ , where Mg is the mass gap and the exponent ξ 0.7 appears to be universal.

We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different bounces off the AdS boundary while the characteristic method can bring us very close to the point of formation of an apparent horizon. Here, we describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of massless scalar fields. We use this scheme to provide more numerical evidence for a recent conjecture on the power-law scaling of the apparent horizon mass resulting from the collapse of subcritical configurations. We also compute the critical exponents and echoing periods for a number of critical points and confirm the expectation that their values should be the same as in the asymptotically-flat case.