广义Darmois-Israel结条件
Generalized Darmois-Israel junction conditions
摘要：
我们提出了一个通用的方法来获得适当的Darmois-Israel结条件的引力理论与高阶导数项通过集成整体运动方程的奇异超曲面。在高阶导数理论中，场方程可以包含比狄拉克δ分布更奇异的项。为了适当地处理它们，我们制定了一个正则化过程的基础上表示的δ函数作为一个序列的经典函数的限制。这个过程涉及到施加适当的约束的外在曲率，使场方程是兼容的奇异源是一个三角洲分布。作为我们方法的明确例子，我们详细演示了如何获得二次引力，$\mathcal{F}(R)$理论，弦论中的4D低能有效作用量和作用量项是欧拉密度的广义连接条件。我们的结果是新颖的，并完善了以前声称的结果在$\mathcal{F} (R)$理论和二次引力的准确性。特别地，当二次引力的耦合常数是Gauss-Bonnet情形的耦合常数时，我们的连接条件退化为后者的已知条件，后者是通过作用量中表面项的边界变化独立获得的。最后，我们简要地讨论了薄壳虫洞和恒星模型的应用。
英文摘要：
We present a general method to derive the appropriate Darmois-Israel junction conditions for gravitational theories with higher-order derivative terms by integrating the bulk equations of motion across the singular hypersurface. In higher derivative theories, the field equations can contain terms which are more singular than the Dirac delta distribution. To handle them appropriately, we formulate a regularization procedure based on representing the delta function as the limit of a sequence of classical functions. This procedure involves imposing suitable constraints on the extrinsic curvature such that the field equations are compatible with the singular source being a delta distribution. As explicit examples of our approach, we demonstrate in detail how to obtain the generalized junction conditions for quadratic gravity, $\mathcal{F}(R)$ theories, a 4D low-energy effective action in string theory and action terms that are Euler densities. Our results are novel, and refine the accuracy of previously claimed results in $\mathcal{F} (R)$ theories and quadratic gravity. In particular, when the coupling constants of quadratic gravity are those for the Gauss-Bonnet case, our junction conditions reduce to the known ones for the latter obtained independently by boundary variation of a surface term in the action. Finally, we briefly discuss a couple of applications to thin-shell wormholes and stellar models.
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