论文标题
关于宇宙空间时间的刚性
On the Rigidity of Cosmological Space-times
论文作者
论文摘要
在本文中，我们分析了一个几何表现良好的宇宙学空间 - $（v^{n+1}，g）$，它们是由本质上类似各向同性的spersurfaces $ \ \ {m_t \} _ {t \ in \ in \ mathbb {r} $ sossers of as a in o n os a a an a an a an a an a a an a ang a a a ang a a a ang a a y a a ang a a y a a ang a a y a a y a gognogy的范围时间状矢量字段$ u $。特别是，这意味着这种空间时间满足了各向同性宇宙学空间时间的几个众所周知的标准，尽管在有问题的家庭中，与$ u $相关的同时空间$（m_t，g_t）$可以作为截面曲率具有截面曲率的签名函数$ k（t）$。在标准宇宙学空间时间的FLRW家族中，这显然是不可能的，它促使我们重新审视文献中各向同性不同定义的几何刚性后果。在此分析中，我们根据所涉及的异构体是（本地）时空（STI空间时间）还是（本地）空间异构体（SI太空时间）为$（m_t，g_t）$的（local）空间异构体（SI太空时间）$。这种微妙的人将被证明至关重要，证明只有当时空异构体被认为是获得与各向同性宇宙空间时间相关的众所周知的刚性特性时。特别是SI空间时间将显示出比STI的类别大的类别，这使一个基本的宇宙学曲率变化模型既不在局部均等。
In this paper we analyse a family of geometrically well-behaved cosmological space-times $(V^{n+1},g)$, which are foliated by intrinsically isotropic space-like hypersurfaces $\{M_t\}_{t\in \mathbb{R}}$, which are orthogonal to a family of co-moving observers defined by a global time-like vector field $U$. In particular, this implies such space-times satisfy several of the well-known criteria for isotropic cosmological space-times, although, in the family in question, the simultaneity-spaces $(M_t,g_t)$ associated to $U$ can have as sectional curvature a sign-changing function $k(t)$. Being this clearly impossible in the FLRW family of standard cosmological space-times, it motivates us to revisit the geometric rigidity consequences of different definitions of isotropy available in the literature. In this analysis, we divide such definition according to whether the isometries involved are taken to be (local) space-time (STI space-times) or (local) space isometries (SI space-times) of $(M_t,g_t)$ for each $t$. This subtlety will be shown to be critical, proving that only when space-time isometries are considered one obtains the well-known rigidity properties associated with isotropic cosmological space-times. In particular SI space-times will be shown to be a strictly larger class than the STI ones, allowing a family of basic cosmological curvature change models which are not even locally isometric to any FLRW space-time.
