We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in $1/D$ upto linear order in the Gauss-Bonnet (GB) parameter $\beta$. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in $1/D$ but non-perturbatively in $\beta$ for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.

中文翻译：

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用于更高导数重力和黑洞第二定律的大 D 膜

我们在更高导数引力的特定理论即爱因斯坦-高斯-博内 (EGB) 引力中推导出双黑洞膜的有效方程，其次导序为 $1/D$ 至高斯-博内 (GB) 中的线性阶) 参数 $\beta$。我们找到了熵流的表达式，该表达式满足该机制中壳上第二定律的局部版本。我们还在 $1/D$ 中推导了最高阶的膜方程，但对于 EGB 重力，在 $\beta$ 中是非微扰的。在这种情况下，我们写下膜的世界体积应力张量的表达式，并计算出静止黑洞的有效膜方程。