Geodesics in stationary spacetimes. Application to Kerr spacetime

通过时状测地线研究标准静态流形的散射刚性

Scattering rigidity for standard stationary manifolds via timelike geodesics

本文通过时状测地线研究标准静态流形的散射刚性问题，利用哈密顿约简证明其与$\mathcal{MP}$-系统散射刚性问题相关，并获得新的刚性结果。

Notes on Five-dimensional Kerr Black Holes

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isospectrum deformations of Ricci-flat Kerr black holes in the sense that the eigenvalues of the Weyl curvature are preserved.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of a celebrated result by R. Bott (Comm. Pure Appl. Math. 9, 1956) we study the Morse index of the iterated of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic $γ$, we prove the existence of a locally constant integer valued map $Λ_γ$ on the unit circle with the property that the Morse index of the iterated $γ^N$ is equal, up to a correction term $ε_γ\in\{0,1\}$, to the sum of the values of $Λ_γ$ at the $N$-th roots of unity. The discontinuit…

Addendum to "Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric", Ann. Inst. H. Poincaré Anal. Non Linéaire, 27 (2010) 857--876

We give the details of the proof of the equality between the critical groups, with respect the H^1 and C^1 topology, at a non-degenerate critical point of the energy functional of a non-reversible Finsler manifold (M,F), defined on the Hilbert manifold of the H^1 curves connecting two given points on M.

非闭合测地线的平稳测地网的通有稠密性

Generic density of stationary geodesic nets that are not closed geodesics

本研究针对维数≥3的闭光滑流形，证明了Baire通有黎曼度量下非闭合测地线的平稳测地网之并集稠密，证实了Nabutovsky-Parsch猜想的对应情形。

On the rigidity of stationary charged black holes: small perturbations of the non-extremal Kerr-Newman family

We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-time must be one of the Kerr-Newman solutions. The closeness to the Kerr-Newman family is measured by the smallness of a pair of Mars-Simon type tensors, which were introduced by Wong in \cite{Wong_09} to detect the Kerr-Newmann family.

Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standard timelike Killing vector field by using Morse theory on the associated Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike…

测地网的Bumpy度量定理

Bumpy Metrics Theorem for Geodesic Nets

本文研究平稳测地网的非退化性问题，证明光滑流形上的Baire泛型黎曼度量下，所有连通嵌入平稳测地网均非退化，推广了闭测地线的相关结果。

沿类时测地线粘合小黑洞 III：真实解的构造与极端质量比并合

Gluing small black holes along timelike geodesics III: construction of true solutions and extreme mass ratio mergers

该研究作为系列工作的第三部分，通过修正近似解构造出沿类时测地线运动的小质量Kerr黑洞的爱因斯坦方程真实解，并将其应用于极端质量比黑洞并合的时空建模。