Testing the black hole no-hair theorem with Galactic Center stellar orbits
Testing the black hole no-hair theorem with Galactic Center stellar orbits
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DOI：
10.1103/physrevd.103.084006
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发表时间：
2020-11
影响因子：
5
通讯作者：
H. Qi;R. O’Shaughnessy;P. Brady
中科院分区：
文献类型：
--
作者：
H. Qi;R. O’Shaughnessy;P. Brady
理论研究提供了原理证明计算，表明银河系中心附近的恒星或脉冲星轨道的测量可以强烈约束银河系中心黑洞，局部物质，甚至引力理论本身的性质。在这项工作中，我们使用马尔可夫链蒙特卡罗方法和费舍尔矩阵来了解恒星轨道和黑洞的参数是受约束的，以及为什么。使用这两种工具，我们得出结论，现有的天体测量不能约束银河系中心黑洞的自旋。根据未来实验的精度和节奏，我们预计黑洞的自旋可以用已知的星星S2来测量。我们的计算表明，我们可以测量无量纲黑洞旋转的准确度和精度为0.1美元，每周测量S2的轨道40年，使用重力望远镜在银河系中心的最佳分辨率。利用Fisher矩阵，从观测策略、星星轨道参数和仪器分辨率三个方面推导了黑洞自旋测量不确定度的解析表达式。我们发现，高偏心率的轨道可以提供更好的约束自旋，具有较高的偏心率的轨道是更有利的，即使当轨道周期较长。此外，如果未来的测量包括发现一个新的，更紧密的恒星轨道，那么未来的数据可以通过直接测量黑洞四极矩来测试强场引力。由于恒星轨道与S2相似，但距离银河系中心的五分之一，以及引力对银河系中心的分辨率限制，我们可以开始用20年的每周测量来检验无毛定理。
Theoretical investigations have provided proof-of-principle calculations suggesting measurements of stellar or pulsar orbits near the Galactic Center could strongly constrain the properties of the Galactic Center black hole, local matter, and even the theory of gravity itself. In this work, we use both Markov chain Monte Carlo method and Fisher matrix to understand what parameters of the stellar orbits and the black hole are well-constrained and why. Using both tools, we conclude that existing astrometric measurements cannot constrain the spin of the Galactic Center black hole. Extrapolating to the precision and cadence of future experiments, we anticipate that the black hole spin can be measured with the known star S2. Our calculations show that we can measure the dimensionless black hole spin to an accuracy and a precision of $\sim$0.1 with weekly measurements of the orbit of S2 for 40 years using the GRAVITY telescope's best resolution at the Galactic Center. We derive an analytic expression for the measurement uncertainty of the black hole spin using Fisher matrix in terms of observation strategy, star's orbital parameters, and instrument resolution. We find that highly eccentric orbit can provide better constraints on the spin, and an orbit with a higher eccentricity is more favorable even when the orbital period is longer. If in addition future measurements include discovery of a new, tighter stellar orbit, then future data could conceivably enable tests of strong field gravity, by directly measuring the black hole quadrupole moment. With a stellar orbit similar to that of S2 but at one fifth the distance to the Galactic Center and GRAVITY's resolution limits on the Galactic Center, we can start to test the no-hair theorem with 20 years of weekly measurements.