论文标题
MOTS稳定性操作员的特征值，用于缓慢旋转Kerr黑洞
Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes
论文作者
论文摘要
我们研究Kerr黑洞的MOTS稳定性操作员的特征值，其角度动量每单位质量$ | a | \ ll m $。我们证明，每个特征值在分析上取决于$ a $（在$ a = 0 $的邻里），并计算其第一个非散文派生。回想一下$ a = 0 $对应于Schwarzschild解决方案，其中每个特征值都有多重性$ 2 \ ell+1 $，我们发现这种退化为非零$ a $。特别是$ 0 <| a | \ ll m $我们获得了一个由$ \ ell $不同的复杂共轭对和一个真实特征值组成的集群。作为我们结果的特殊情况，我们获得了一个简单的公式，以实现主要特征值的变化。对于保留黑洞总面积或质量的扰动，我们发现主要特征值在$ a = 0 $的局部最大值。但是，在其他扰动中，主要特征值在$ a = 0 $的局部最低限度。
We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass $|a| \ll M$. We prove that each eigenvalue depends analytically on $a$ (in a neighbourhood of $a=0$), and compute its first nonvanishing derivative. Recalling that $a=0$ corresponds to the Schwarzschild solution, where each eigenvalue has multiplicity $2\ell+1$, we find that this degeneracy is completely broken for nonzero $a$. In particular, for $0 < |a| \ll M$ we obtain a cluster consisting of $\ell$ distinct complex conjugate pairs and one real eigenvalue. As a special case of our results, we get a simple formula for the variation of the principal eigenvalue. For perturbations that preserve the total area or mass of the black hole, we find that the principal eigenvalue has a local maximum at $a=0$. However, there are other perturbations for which the principal eigenvalue has a local minimum at $a=0$.
