Viscous Asymptotically Flat Reissner-Nordstr\"om Black Branes

We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.Comment: 28 pages, 2 figure. v3: Small changes and a few typos correcte

Probing the Hydrodynamic Limit of (Super)gravity

We study the long-wavelength effective description of two general classes of charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes in ten and eleven dimensional supergravity. In particular, we consider gravitational brane solutions in a hydrodynamic derivative expansion (to first order) for arbitrary dilaton coupling and for general brane and co-dimension and determine their effective electro-fluid-dynamic descriptions by exacting the characterizing transport coefficients. We also investigate the stability properties of the corresponding hydrodynamic systems by analyzing their response to small long-wavelength perturbations. For branes carrying unsmeared charge, we find that in a certain regime of parameter space there exists a branch of stable charged configurations. This is in accordance with the expectation that D/NS/M-branes have stable configurations, except for the D5, D6, and NS5. In contrast, we find that Maxwell charged brane configurations are Gregory-Laflamme unstable independently of the charge and, in particular, verify that smeared configurations of D0-branes are unstable. Finally, we provide a modification to the mapping presented in arxiv:1211.2815 and utilize it to provide a non-trivial cross-check on a certain subset of our transport coefficients with the results of arXiv:1110.2320.Comment: 36 pages, 2 figures. v2: Added reference and corrected typ

Null-Wave Giant Gravitons from Thermal Spinning Brane Probes

We construct and analyze thermal spinning giant gravitons in type II/M-theory based on spherically wrapped black branes, using the method of thermal probe branes originating from the blackfold approach. These solutions generalize in different directions recent work in which the case of thermal (non-spinning) D3-brane giant gravitons was considered, and reveal a rich phase structure with various new properties. First of all, we extend the construction to M-theory, by constructing thermal giant graviton solutions using spherically wrapped M2- and M5-branes. More importantly, we switch on new quantum numbers, namely internal spins on the sphere, which are not present in the usual extremal limit for which the brane world volume stress tensor is Lorentz invariant. We examine the effect of this new type of excitation and in particular analyze the physical quantities in various regimes, including that of small temperatures as well as low/high spin. As a byproduct we find new stationary dipole-charged black hole solutions in AdS_m X S^n backgrounds of type II/M-theory. We finally show, via a double scaling extremal limit, that our spinning thermal giant graviton solutions lead to a novel null-wave zero-temperature giant graviton solution with a BPS spectrum, which does not have an analogue in terms of the conventional weakly coupled world volume theory.Comment: v1: 31p

Thermal Giant Gravitons

We study the giant graviton solution as the AdS_5 X S^5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S^3 moving on the S^5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S^3. We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS_5 part.Comment: v1: 32 pages + 11 pages appendices, 13 figures, v2: typos fixed in Sec.2 and other misprints, references adde

Dissipative hydrodynamics with higher-form symmetry

A theory of parity-invariant dissipative fluids with q-form symmetry is formulated to first order in a derivative expansion. The fluid is anisotropic with symmetry SO(D − 1 − q) × SO(q) and carries dissolved q-dimensional charged objects that couple to a (q + 1)-form background gauge field. The case q = 1 for which the fluid carries string charge is related to magnetohydrodynamics in D = 4 spacetime dimensions. We identify q+7 parity-even independent transport coefficients at first order in derivatives for q > 1. In particular, compared to the q = 1 case under the assumption of parity and charge conjugation invariance, fluids with q > 1 are characterised by q extra transport coefficients with the physical interpretation of shear viscosity in the SO(q) sector and current resistivities. We discuss certain issues related to the existence of a hydrostatic sector for fluids with higher-form symmetry for any q ≥ 1. We extend these results in order to include an interface separating different fluid phases and study the dispersion relation of capillary waves finding clear signatures of anisotropy. The formalism developed here can be easily adapted to study hydrodynamics with multiple higher-form symmetries

Forced Fluid Dynamics from Blackfolds in General Supergravity Backgrounds

We present a general treatment of the leading order dynamics of the collective modes of charged dilatonic p-brane solutions of (super) gravity theories in arbitrary backgrounds. To this end we employ the general strategy of the blackfold approach which is based on a long-wavelength derivative expansion around an exact or approximate solution of the (super)gravity equations of motion. The resulting collective mode equations are formulated as forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive them in full generality (including all possible asymptotic fluxes and dilaton profiles) in a far-zone analysis of the (super)gravity equations and in representative examples in a near-zone analysis. An independent treatment based on the study of external couplings in hydrostatic partition functions is also presented. Special emphasis is given to the forced collective mode equations that arise in type IIA/B and eleven-dimensional supergravities, where besides the standard Lorentz force couplings our analysis reveals additional couplings to the background, including terms that arise from Chern-Simons interactions. We also present a general overview of the blackfold approach and some of the key conceptual issues that arise when applied to arbitrary backgrounds