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

Abstract 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 an upper bound on the Gauss–Bonnet coupling constant in the AdS space. Causality constrains the value of Gauss–Bonnet coupling constant $$\alpha _{GB}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi>GB</mml:mi></mml:mrow></mml:msub></mml:math> to be bounded by $$\alpha _{GB}\le 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi>GB</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> as $$D\rightarrow 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> .

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