用李雅普诺夫指数检验广义相对论
Lyapunov Exponents to Test General Relativity
AI总结：
本文提出一个稳健数值框架，用于计算并比较Kerr时空与任意修改引力理论中类光测地线的李雅普诺夫指数，并在标量Gauss-Bonnet引力和动力学Chern-Simons引力中给出结果，进而确定甚长基线干涉测量约束这些理论所需的精度下界。
摘要：
光子环是近未来天基甚长基线干涉测量任务的关键观测目标。在相邻光环之间测得的通量比值由相应近束缚类光测地线的李雅普诺夫指数刻画。因此，理解这一环境中的李雅普诺夫指数对于理解黑洞观测至关重要，特别是它们可能为约束修改引力理论提供一条途径。虽然近期工作已在描述Kerr时空中的这些测地线方面取得重要进展，但一种与理论无关的描述因李雅普诺夫指数依赖于时间参数化而变得复杂，这要求在比较两种不同理论中的这些指数时必须格外小心。在本工作中，我们提出一个稳健的数值框架，用于计算并比较Kerr时空中类光测地线的李雅普诺夫指数与任意修改引力理论中的相应指数。随后，我们给出在两种特定有效理论——标量Gauss-Bonnet引力和动力学Chern-Simons引力——中计算类光测地线李雅普诺夫指数所得到的结果。利用该框架，我们确定了在甚长基线干涉测量观测能够约束这些理论之前所需达到的精度下界。
英文摘要：
Photon rings are key targets for near-future space-based very-long baseline interferometry missions. The ratio of flux measured between successive light-rings is characterized by the Lyapunov exponents of the corresponding nearly-bound null geodesics. Therefore, understanding Lyapunov exponents in this environment is of crucial importance to understanding black hole observations in general, and in particular, they may offer a route for constraining modified theories of gravity. While recent work has made significant progress in describing these geodesics for Kerr, a theory-agnostic description is complicated by the fact that Lyapunov exponents are time-parameterization dependent, which necessitates care when comparing these exponents in two different theories. In this work, we present a robust numerical framework for computing and comparing the Lyapunov exponents of null geodesics in Kerr with those in an arbitrary modified theory. We then present results obtained from calculating the Lyapunov exponents for null geodesics in two particular effective theories, scalar Gauss-Bonnet gravity and dynamical Chern-Simons gravity. Using this framework, we determine accuracy lower-bounds required before a very-long baseline interferometry observation can constrain these theories.
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