论文标题
关于复杂指标，复杂时间和周期性宇宙的注意
Note on complex metrics, complex time and periodic universes
论文作者
论文摘要
一方面是由等质动力学系统的最新结果，另一方面是由复杂指标的量子重力应用的动机，我们表明，如果考虑了这样的扩大的指标，则可以轻松获得Einstein方程的周期性或弹跳复杂解决方案。发现，对于任何给定的解决方案，爱因斯坦方程的$ g_ {μν} $，通过复杂的时间变化，可以构建与$ g_ {μ{μ的g_ {μ的g_ {μν} $无限的周期性或弹跳的复杂解决方案$ \ hat g_ {μNν} $，而不是$ g_ {μ{μ{μ{μ的长度时间间隔。这些结果基于复杂的差异性的使用，指出了该理论中不可接受的任意性。如我们所示，在[M. Kontsevich和G. B. Segal，Q。J. Math。 72，673（2021）]，并在[E. Witten，Arxiv：2111.06514]解决了这个问题，限制了可允许的复杂差异性的家族。我们得出的结论是，这种情况可以被视为对等效原理对复杂空间时间的量子重力概括。
Motivated on the one hand by recent results on isochronous dynamical systems, and on the other by quantum gravity applications of complex metrics, we show that, if such enlarged class of metrics is considered, one can easily obtain periodic or bouncing complex solutions of Einstein's equations. It is found that, for any given solution $g_{μν}$ of the Einstein's equations, by means of a complex change of time, one can construct infinitely many periodic or bouncing complex solutions $\hat g_{μν}$ that are physically indistinguishable from $g_{μν}$ over an arbitrarily long time interval. These results, that are based on the use of complex diffeomorphisms, point out an unacceptable arbitrariness in the theory. As we will show, a condition on the class of physically meaningful complex metrics proposed in [M. Kontsevich and G. B. Segal, Q. J. Math. 72, 673 (2021)] and discussed in [E. Witten, arXiv:2111.06514] solves this problem, restricting the family of admissible complex diffeomorphisms. We conclude arguing that this condition can be viewed as a quantum-gravity generalization of the equivalence principle to complex space-times.
