纯Lovelock引力中的外禀黑洞唯一性
Extrinsic black hole uniqueness in pure Lovelock gravity
摘要：
我们定义了一个外生黑洞的概念，在纯Lovelock引力度$k$，它捕捉了所谓的Lovelock-Schwarzschild解决方案的基本特征，被视为旋转不变的超曲面与零$2k$ -中曲率在欧几里得空间$\mathbb R^{n+1}$，$2\leq 2k\leq n-1$。然后我们结合正则性论证和Araújo-Leite的刚性结果，在自然的椭圆性条件下证明了这类黑洞的全局唯一性定理。作为结果，我们得到，在相应的Penrose不等式的图形建立的Ge-Wang-Wu，局部刚性结果的Lovelock-Schwarzschild解决方案。
英文摘要：
We define a notion of extrinsic black hole in pure Lovelock gravity of degree $k$ which captures the essential features of the so-called Lovelock-Schwarzschild solutions, viewed as rotationally invariant hypersurfaces with null $2k$-mean curvature in Euclidean space $\mathbb R^{n+1}$, $2\leq 2k\leq n-1$. We then combine a regularity argument with a rigidity result by Araújo-Leite to prove, under a natural ellipticity condition, a global uniqueness theorem for this class of black holes. As a consequence we obtain, in the context of the corresponding Penrose inequality for graphs established by Ge-Wang-Wu, a local rigidity result for the Lovelock-Schwarzschild solutions.
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