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arXiv 1307.0504hep-thgr-qc
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带电黑膜的电弹性

Electroelasticity of Charged Black Branes

Jay Armas, Jakob Gath, Niels A. Obers

摘要:

本文给出了带有高阶电荷的流体膜的一阶修正动力学,得到了它们的运动方程的一般形式,使之达到极-偶极阶。假设线性响应理论,我们表征了相应的有效理论的静态弯曲充电(一个)各向同性流体膜的两套响应系数,杨氏模量和压电模量。随后,我们发现大类的例子,在重力的这种有效的理论,通过构建静态应变带电黑膜解决方案,一阶导数扩展。利用解生成技术,以弯曲中性黑膜为种子解,得到了Einstein-Maxwell-Einstein-Maxwell引力中一类带涂抹Maxwell荷的带电黑膜几何.在10维时空的特殊情况下,我们进一步使用T-对偶来产生具有更高形式电荷的弯曲黑膜,包括II型弦论的涂抹D-膜。通过随后测量的弯曲力矩和电偶极矩,这些几何形状获得由于应变,我们发现,它们的形式被捕获的经典电弹性理论。特别是,我们发现,我们的应变带电黑膜解决方案的杨氏模量和压电模量参数化的共4个响应系数,无论是各向同性以及各向异性的情况下。

英文摘要:

We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. 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. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.

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