Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Abstract

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension $d$, exponents $z$ and $\theta$. Remarkably, the case $d=\theta$ and $z=2$ is a very special in that the charge diffusion $D_c$ is a constant and the energy diffusion $D_e$ might be ill-defined, but $v_B^2\tau$ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

30 pages, 2 figures

References in corpus (28)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Theory of universal incoherent metallic transport
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• The complete $1/N$ expansion of a SYK--like tensor model
• Supersymmetric SYK model and random matrix theory
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Towards a 2d QFT Analog of the SYK Model
• A Supersymmetric SYK-like Tensor Model
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Three Dimensional View of the SYK/AdS Duality
• Charge diffusion and the butterfly effect in striped holographic matter
• Chiral anomalies and AdS/CMT in two dimensions
• Random Matrices and Holographic Tensor Models
• Higher derivative corrections to incoherent metallic transport in holography
• Diffusivities bounds and chaos in holographic Horndeski theories
• Anisotropic plasma at finite $U(1)$ chemical potential
• Vector models and generalized SYK models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• On Butterfly effect in Higher Derivative Gravities
• Disorder in the Sachdev-Yee-Kitaev Model
• Anisotropic plasma with a chemical potential and scheme-independent instabilities
• DC Conductivities with Momentum Dissipation in Horndeski Theories
• Holographic Heat Current as Noether Current
• Matrix Quantum Mechanics from Qubits

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• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
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• On pole-skipping with gauge-invariant variables in holographic axion theories
• Stationary equilibrium of test particles near charged black branes with the hyperscaling violating factor
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