论文标题
黑洞拓扑应用的贝克里 - 梅里几乎分裂的结果
A Bakry-Émery Almost Splitting Result With Applications to the Topology of Black Holes
论文作者
论文摘要
在几乎非负通用的$ m $ -bakry-émery-émeryricci曲率的情况下，建立了几乎分裂的定理，其中$ m $是正的，并且相关的向量场不一定是函数梯度的必不可少的。在这种情况下，表明直径上限和体积下限，这种歧管的基本组几乎是Abelian。此外，对于RICCI曲率下限的众所周知结果的扩展是针对广义$ M $ -Bakry-émeryRicci曲率的。其中包括：Gromov和Gallot的第一个Betti数字，Anderson对基本组同构类型的有限性，体积比较，Abresch Gromoll不平等和Cheng-Yau梯度估计。最后，该分析应用于较高维度的固定真空黑洞，以发现低温层必须具有有限的拓扑结构，类似于（极端）零温度的限制。
The almost splitting theorem of Cheeger-Colding is established in the setting of almost nonnegative generalized $m$-Bakry-Émery Ricci curvature, in which $m$ is positive and the associated vector field is not necessarily required to be the gradient of a function. In this context it is shown that with a diameter upper bound and volume lower bound the fundamental group of such manifolds is almost abelian. Furthermore, extensions of well-known results concerning Ricci curvature lower bounds are given for generalized $m$-Bakry-Émery Ricci curvature. These include: the first Betti number bound of Gromov and Gallot, Anderson's finiteness of fundamental group isomorphism types, volume comparison, the Abresch-Gromoll inequality, and a Cheng-Yau gradient estimate. Finally, this analysis is applied to stationary vacuum black holes in higher dimensions to find that low temperature horizons must have limited topology, similar to the restrictions exhibited by (extreme) horizons of zero temperature.
