Note on Noether charge and holographic transports

Abstract

We clarify the relation between the Noether charge associated to an arbitrary vector field and the equations of motions by revisiting Wald formalism. For a time-like Killing vector, aspects of the Noether charge suggest that it is dual to the heat current in the boundary for general holographic theories. For a space-like Killing vector, we interpret the Noether charge (at the transverse direction) as shear stress of the dual fluid so we can compute the ratio of shear viscosity to entropy density by simply using the infrared data on the black hole event horizon. We test the new method for Einstein gravity and Gauss-Bonnet gravity and find that it produces correct results for both cases even in the presence of additional matter fields.

v2, add an appendix discuss viscosity bound and causality violation

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Cited by in corpus (8)

• Holographic complexity and thermodynamics of AdS black holes
• Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions
• Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories
• Time dependence of complexity for Lovelock black holes
• Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity
• Holographic complexity under a global quantum quench
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Holographic Aspects of Quasi-topological Gravity