Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes
Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes
复制标题
DOI：
10.1103/physrevd.106.124036
复制
发表时间：
2022-09
影响因子：
5
通讯作者：
S. Völkel;N. Franchini;E. Barausse;E. Berti
中科院分区：
文献类型：
--
作者：
S. Völkel;N. Franchini;E. Barausse;E. Berti
在修正的引力理论中，描述非旋转黑洞扰动的类薛定谔方程中出现的势也被修正了。在本文中，我们提出了一个问题：这些修正是否可以用黑洞准正态模频率的高精度引力波测量来约束？我们将这些修正扩展到一个调节偏离广义相对论势的小扰动参数中，并以M/r为幂。我们计算了在扰动参数下二阶修正势的拟正态模态。然后，我们使用马尔可夫链-蒙特卡罗（MCMC）方法，在“乐观”的情况下，我们一次改变一个系数，在“悲观”的情况下，我们同时改变它们，以恢复M/r展开中的系数。在这两种情况下，我们发现单个参数的边界都不是鲁棒的。由于准正态模频率与光环附近的扰动势的行为有关，我们提出了一种不同的策略。受WKB （Wentzel-Kramers-Brillouin）理论的启发，我们证明了势及其二阶导数在光环上的值可以被鲁棒约束。这些限制允许在基于黑洞光谱的测试和事件视界望远镜和未来仪器对黑洞“阴影”的观测之间进行更直接的比较。
In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of non-rotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole's quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain-Monte-Carlo (MCMC) methods to recover the coefficients in the $M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time, and in a ``pessimistic'' scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole `shadows'' by the Event Horizon Telescope and future instruments.