Causality of black holes in 4-dimensional Einstein-Gauss-Bonnet-Maxwell theory

We study charged black hole solutions in 4-dimensional (4D) Einstein-Gauss-Bonnet-Maxwell theory to the linearized perturbation level. We first compute the shear viscosity to entropy density ratio. We then demonstrate how bulk causal structure analysis imposes a upper bound on the Gauss-Bonnet coupling constant in the AdS space. Causality constrains the value of Gauss-Bonnet coupling constant $α_{GB}$ to be bounded by $α_{GB}\leq 0$ as $D\rightarrow 4$.

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