Killing tensors in stationary and axially symmetric space-times

三价Killing张量在Weyl类定常轴对称时空中的约化

Reducibility of Valence-3 Killing Tensors in Weyl's Class of Stationary and Axially Symmetric Space-Times

稳态和轴对称时空在天体物理学中扮演着重要的角色，特别是在中子星和黑洞理论中。这些时空的静态真空子类被称为外尔类，其中最突出的例子就是史瓦西时空。本文研究了Weyl类时空中三价Killing张量场空间。Killing张量场在物理学中起着至关重要的作用，因为它们对应于测地线运动的不变量（即运动常数）。证明了在静态轴对称真空时空中，三价Killing张量场空间是由Killing向量场和二次Killing张量场生成的.利用这个结果，证明了对于Zipoy-Voorhees度量族，三价Killing张量场总是由Killing向量场和度量生成的.

Einstein-麦克斯韦方程组的N-黑洞定态解和轴对称解

N-Black Hole Stationary and Axially Symmetric Solutions of the Einstein-Maxwell Equations

爱因斯坦/麦克斯韦方程组在静止和轴对称的情况下简化为具有指定奇点的调和映射：R^3Σ-> H^2_C，其中Σ是对称轴的子集，H^2_C是复双曲平面。受这个问题的启发，我们证明了具有给定奇点φ：R^n <$-> H的调和映射的存在性和唯一性，其中Sigma是R^n的余维至少为2的子流形，H是非紧型秩为1的经典黎曼全局对称空间.这个结果，当应用到黑洞问题，产生的解决方案，可以被解释为平衡配置的多个同轴旋转的带电黑洞保持分开的奇异支柱。

定常真空时空Killing向量在边界上的唯一延拓与扩张

Unique continuation and extensions of Killing vectors at boundaries for stationary vacuum space-times

推广了Anderson-Herzlich和Biquard的黎曼定理，我们证明了两个$(n+1)$维定态真空时空（可能具有宇宙常数$Λ\in \R$）沿类时超曲面$\mycal T$在一阶上重合，在$\mycal T$的邻域内等距.进一步证明了$\partial M$的KIDS可以推广到$\partial M$附近的Killing向量.在AdS类型的设置中，我们证明了唯一连续的共形无穷远附近的度量具有相同的共形无穷远和相同的待定项。本文还建立了保形无穷远的保形Killing向量在$\partial M$附近的延拓，使待定Festhman-Graham项保持不变.

On Finsler spacetimes with a timelike Killing vector field

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finsleria…

因果Killing向量的单调性与ADM质量极小化子的几何

Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers

本文研究了ADM质量极小化初始数据集，证明了正质量定理等号情形与正Bartnik质量极小化子的时空嵌入性质，并利用因果Killing向量场Lorentzian长度的新单调性公式证实了Bartnik平稳真空猜想。

Stationary Vacuum Black Holes in 5 Dimensions

We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a prime $3$-manifold of positive Yamabe type, namely the $3$-sphere $S^3$, the ring $S^1\times S^2$, or the lens space $L(p,q)$. The Einstein vacuum equations reduce to an axially symmetric harmonic map with prescribed singularities from $\mathbb{R}^3$ into the symmetric space $SL(3,\mathbb{R})/SO(3)$. In this paper, we solve the problem for all possible topologi…