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Surface term, corner term, and action growth in F(Rabcd) gravity theory

机译：F（Rabcd）重力理论中的表面项，角项和作用增长

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摘要

After reformulating F ( Riemann ) gravity theory as a second derivative theory by introducing two auxiliary fields to the bulk action, we derive the surface term as well as the corner term supplemented to the bulk action for a generic nonsmooth boundary such that the variational principle is well posed. We also introduce the counterterm to make the boundary term invariant under the reparametrization for the null segment. Then as a demonstration of the power of our formalism, not only do we apply our expression for the full action to evaluate the corresponding action growth rate of the Wheeler-DeWitt patch in the Schwarzchild anti–de Sitter black hole for the F ( R ) gravity and critical gravity, where the corresponding late time behavior recovers the previous one derived by other approaches, but also in the asymptotically anti–de Sitter black hole for the critical Einsteinian cubic gravity, where the late time growth rate vanishes but still saturates the Lloyd bound.
机译：在通过将两个辅助场引入体作用将F（Riemann）引力理论重新构造为二阶导数理论之后，我们推导了对一般非光滑边界的体作用补充的表面项和角项。摆好姿势。我们还介绍了反条件项，以使空项的重新参数化下的边界项不变。然后，为了证明我们形式主义的力量，我们不仅将完整动作的表达式应用于评估F（R）在Schwarzchild anti-de Sitter黑洞中Wheeler-DeWitt贴片的相应动作增长率。重力和临界重力，相应的后期行为恢复了其他方法得出的前一个行为，但在临界爱因斯坦立方重力中也渐近地反de Sitter黑洞，其中后期增长速度消失但仍使劳埃德饱和界。

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