论文标题
静态真空的5维空间周期溶液
5-Dimensional Space-Periodic Solutions of the Static Vacuum Einstein Equations
论文作者
论文摘要
关于迈尔斯的猜想是关于存在5维常规静态真空解决方案的肯定答案，这些静态真空解决方案平衡了无限数量的黑洞，这些黑洞具有Kasner渐近性。构建了各种示例，具有不同的ring $ s^1 \ times s^2 $的组合和$ s^3 $横截面范围。此外，我们显示了具有Kasner渐近学的5维真空孔的存在。这些是常规的静态空间周期性真空空位，没有黑洞。因此，我们还获得了尺寸4中非负RICCI曲率的完整riemannian歧管的新示例，在维度5中，零RICCI曲率在Dimension 5中，任意较大和无限的第二Betti数字。
An affirmative answer is given to a conjecture of Myers concerning the existence of 5-dimensional regular static vacuum solutions that balance an infinite number of black holes, which have Kasner asymptotics. A variety of examples are constructed, having different combinations of ring $S^1\times S^2$ and sphere $S^3$ cross-sectional horizon topologies. Furthermore, we show the existence of 5-dimensional vacuum solitons with Kasner asymptotics. These are regular static space-periodic vacuum spacetimes devoid of black holes. Consequently, we also obtain new examples of complete Riemannian manifolds of nonnegative Ricci curvature in dimension 4, and zero Ricci curvature in dimension 5, having arbitrarily large as well as infinite second Betti number.
