Antoniadis I, Cotsakis S, Klaoudatou I
Laboratoire de Physique Théorique et Hautes Energies - LPTHE, Sorbonne Université, CNRS 4 Place Jussieu, Paris 75005, France.
Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, Moscow 117198, Russia.
Philos Trans A Math Phys Eng Sci. 2022 Aug 22;380(2230):20210180. doi: 10.1098/rsta.2021.0180. Epub 2022 Jul 4.
We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a 'perfect fluid' with an equation of state [Formula: see text], where [Formula: see text] is the 'pressure' and [Formula: see text] is the 'density' of the fluid, depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane for [Formula: see text] or of AdS branes for [Formula: see text]. More cases can be found by gluing two regular brunches of solutions at the position of the brane. However, only a flat brane for [Formula: see text] leads to finite Planck mass on the brane and thus localizes gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane and a range of [Formula: see text], which is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state of the form [Formula: see text] with [Formula: see text] and [Formula: see text]. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.
我们回顾了关于嵌入五维体空间中的一个三膜（平坦或弯曲）的奇点结构和渐近分析的研究，该五维体空间充满了一种状态方程为[公式：见文本]的“理想流体”，其中[公式：见文本]是流体的“压强”，[公式：见文本]是流体的“密度”，它们取决于第五个空间坐标。在体空间中满足正能量条件的正则解仅在以下情形存在：对于[公式：见文本]，是平坦膜的情形；对于[公式：见文本]，是反德西特（AdS）膜的情形。通过在膜的位置胶合两个正则解分支，可以找到更多情形。然而，只有对于[公式：见文本]的平坦膜会导致膜上的普朗克质量有限，从而使引力局域化。在最近的一项工作中，我们表明，一种修正先前结果并获得一个针对平坦膜以及一系列[公式：见文本]的解的方法，该解既没有有限距离奇点，又与四维普朗克质量的能量和有限性的物理条件兼容，即通过引入一个满足形式为[公式：见文本]的非线性状态方程的体流体分量，其中[公式：见文本]且[公式：见文本]。本文是主题为“数学宇宙学的未来，第2卷”的一部分。
