天体系统在 Chern-Simons 引力理论中演化过程的数值模拟

Chern-Simons（CS）引力是一个在广义相对论中加入破坏宇称守恒项进而对其进行修正的引力理论。这些修正是弦理论和圈量子引力理论所必需的，所以CS引力的实验验证或否定会为它们的正确与否提供重要证据。由于修正项在强引力场中才会变得重要，对黑洞或如中子星这样的致密天体进行天文观测无疑是最佳的实验策略。而开展观测需要先期展开大量理论研究，以构建有效的观测方案和数据挖掘手段。只有数值模拟能够对例如双黑洞合并这种信号较强的在真实的复杂天文环境中发生的天文现象进行有效理论研究。但遗憾的是，由于种种迹象显示CS引力理论不具备适定性，对其进行模拟的努力尚未成功。我们在本项目中提议将CS扩展成一个具备适定性的可模拟的理论（其模拟结果仍是原始CS理论的解），进而解决这个难题。本项目包括如下步骤：发展拓展理论、编写并运行数值代码来模拟单和双黑洞系统、根据模拟中获得的电磁和引力波信号构建观测方案等。

Chern-Simons（CS）gravity is a modification of general relativity that involves the introduction of parity-violating higher derivative terms. The addition of these terms is recognized as being necessary for the self-consistency of both string theory and loop quantum gravity, and so verifying or ruling out CS gravity will provide strong evidence for or against these leading candidates for quantizing gravity. As the parity-violating terms become important in strong gravity regimes, astronomical observations of black holes and compact stars such as neutron stars constitute the best experimental strategy. Before the observations can take place however, extensive theoretical studies of the dynamics of these objects and associated radiation mechanism within CS gravity have to be carried out, so that effective observational strategies can be devised and template-based data analysis be made possible. Only numerical simulations can tackle the most astronomically interesting scenarios such as binary black hole mergers, but due to the CS gravity (in all likelihood) being ill-posed, its numerical simulation has remained an outstanding problem. In this proposal, we suggest a novel method for extending the CS gravity into a well-posed theory, as well as the means to recover the solutions of the original CS theory. The proposed study includes several stages: the analytical development of the extended theory; the implementation of the numerical code, and the simulation of simpler single-black-hole and more complex binary-black-hole systems; and finally utilizing the electromagnetic and gravitational radiation signals obtained from the simulations to devise observational strategies, geared especially towards the upcoming completion of large Chinese telescopes and the second generation gravitational wave detectors worldwide.