Abstract
We consider long-wavelength perturbations of charged black branes to first order in a uidelastic derivative expansion. At first order the perturbations decouple and we treat the hydrodynamic and elastic perturbations separately. To put the results in a broader perspective, we present the rst-order corrected dynamics of uid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order in the absence of external forces. To monopole order, we characterize the corresponding effective theory of viscous uid branes by writing down the general form of the first-order dissipative corrections in terms of the shear and bulk viscosities as well as the transport coefficient associated with charge di
usion. To dipole order, we furthermore, applying linear response theory, characterize the corresponding effective theory of stationary bent charged (an)isotropic uid branes in terms of two sets of response coecients, the Young modulus and the piezoelectric moduli. We subsequently consider a large class of examples in gravity of this effective theory. In particular, we consider dilatonic black p-branes in two different settings: charged under a Maxwell gauge eld and charged under a (p+1)-form gauge field, including the D-branes and M-branes of type II string theory and M theory, respectively. Using familiar techniques, we compute the associated transport coecients and uncover how the shear and bulk viscosities are modified in the presence of electric charge and a dilaton coupling. For the case of Maxwell black branes we furthermore compute the charge diffusion constant. We find that the shear viscosity to entropy bound is saturated and comment on proposed bounds for the bulk viscosity to entropy ratio. With the transport coecients we compute the first-order dispersion relations of the effective uid and analyze the dynamical stability of the black branes. We then focus on constructing stationary strained charged black brane solutions to rst order in a derivative expansion. Using solution generating techniques and the bent neutral black brane as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton theory. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. We compute the bending moment and the electric dipole moment which these solutions acquire due to the strain and uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of the strained charged black brane solutions are parameterized by a total of four response coecients, both for the isotropic as well as for the anisotropic cases.
usion. To dipole order, we furthermore, applying linear response theory, characterize the corresponding effective theory of stationary bent charged (an)isotropic uid branes in terms of two sets of response coecients, the Young modulus and the piezoelectric moduli. We subsequently consider a large class of examples in gravity of this effective theory. In particular, we consider dilatonic black p-branes in two different settings: charged under a Maxwell gauge eld and charged under a (p+1)-form gauge field, including the D-branes and M-branes of type II string theory and M theory, respectively. Using familiar techniques, we compute the associated transport coecients and uncover how the shear and bulk viscosities are modified in the presence of electric charge and a dilaton coupling. For the case of Maxwell black branes we furthermore compute the charge diffusion constant. We find that the shear viscosity to entropy bound is saturated and comment on proposed bounds for the bulk viscosity to entropy ratio. With the transport coecients we compute the first-order dispersion relations of the effective uid and analyze the dynamical stability of the black branes. We then focus on constructing stationary strained charged black brane solutions to rst order in a derivative expansion. Using solution generating techniques and the bent neutral black brane as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton theory. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. We compute the bending moment and the electric dipole moment which these solutions acquire due to the strain and uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of the strained charged black brane solutions are parameterized by a total of four response coecients, both for the isotropic as well as for the anisotropic cases.
| Original language | English |
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| Publisher | The Niels Bohr Institute, Faculty of Science, University of Copenhagen |
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| Number of pages | 100 |
| Publication status | Published - 2013 |