论文标题
固定的轴对称爱因斯坦 - 维拉索夫分叉的Kerr Spacetime
Stationary axisymmetric Einstein-Vlasov bifurcations of the Kerr spacetime
论文作者
论文摘要
我们构建了一个固定轴对称性和渐近平坦的空间解决方案的单参数家族，以从Kerr Spacetime分叉的Einstein-Vlasov系统。构造的解决方案具有该物质的空间支持的特性，是远离黑洞的有限的轴对称壳。我们的证明主要是基于对靠近Kerr的固定轴对称空间的一组固定轴向测量学的分析，那里的大地测量流不一定是可集成的。此外，对爱因斯坦田间方程的分析依赖于Chodosh和Shlapentokh-Rothman开发的修改后的Carter Robinson理论。这提供了在轴对称情况下对爱因斯坦 - 维拉索夫系统的首次构造，并概括了在球体对称的情况下已经完成的结构。
We construct a one-parameter family of stationary axisymmetric and asymptotically flat spacetimes solutions to the Einstein-Vlasov system bifurcating from the Kerr spacetime. The constructed solutions have the property that the spatial support of the matter is a finite, axisymmetric shell located away from the black hole. Our proof is mostly based on the analysis of the set of trapped timelike geodesics for stationary axisymmetric spacetimes close to Kerr, where the geodesic flow is not necessarily integrable. Moreover, the analysis of the Einstein field equations relies on the modified Carter Robinson theory developed by Chodosh and Shlapentokh-Rothman. This provides the first construction of black hole solutions to the Einstein-Vlasov system in the axisymmetric case and generalises the construction already done in the spherically symmetric case.
