论文标题
在参数化框架中准确地映射球形对称黑洞
Accurate mapping of spherically symmetric black holes in a parameterised framework
论文作者
论文摘要
Rezzolla-Zhidenko（RZ）框架提供了一种有效的方法，可以使用少量变量在任意重力理论中表征球形对称的黑洞空位[L. Rezzolla和A. Zhidenko，物理。 Rev. D. 90，084009（2014）]。这些变量可以原则上从各种天体物理过程的近摩尼子测量值中获得，从而有可能对黑洞特性以及强场策略中的一般相对性理论有效测试。在这里，我们扩展了此框架，以允许任意渐近流量，球面对称度量标准的参数化，并介绍11维（11D）参数化空间$π$的概念，每个解决方案都可以在其上可视化为曲线或表面。 $ \ mathscr {l}^2 $ norm在此空间上用于测量特定紧凑的对象解决方案与Schwarzschild黑洞解决方案的偏差。我们在此框架内计算了与粒子和光子轨道相关的各种可观察结果，并证明我们获得的相对误差很低（大约$ 10^{ - 6} $）。 In particular, we obtain the innermost stable circular orbit (ISCO) frequency, the unstable photon-orbit impact parameter (shadow radius), the entire orbital angular speed profile for circular Kepler observers and the entire lensing deflection angle curve for various types of compact objects, including non-singular and singular black holes, boson stars and naked singularities, from various theories of gravity.最后，我们以表格形式提供了描述各种常用的黑洞空间所需的四阶RZ参数化的前11个系数。与天体物理可观察到的一阶RZ参数化（例如ISCO频率）进行比较时，此处提供的系数提高了两个数量级或更多阶的精度。
The Rezzolla-Zhidenko (RZ) framework provides an efficient approach to characterize spherically symmetric black-hole spacetimes in arbitrary metric theories of gravity using a small number of variables [L. Rezzolla and A. Zhidenko, Phys. Rev. D. 90, 084009 (2014)]. These variables can be obtained in principle from near-horizon measurements of various astrophysical processes, thus potentially enabling efficient tests of both black-hole properties and the theory of general relativity in the strong-field regime. Here, we extend this framework to allow for the parametrization of arbitrary asymptotically-flat, spherically symmetric metrics and introduce the notion of a 11-dimensional (11D) parametrization space $Π$, on which each solution can be visualised as a curve or surface. An $\mathscr{L}^2$ norm on this space is used to measure the deviation of a particular compact object solution from the Schwarzschild black-hole solution. We calculate various observables, related to particle and photon orbits, within this framework and demonstrate that the relative errors we obtain are low (about $10^{-6}$). In particular, we obtain the innermost stable circular orbit (ISCO) frequency, the unstable photon-orbit impact parameter (shadow radius), the entire orbital angular speed profile for circular Kepler observers and the entire lensing deflection angle curve for various types of compact objects, including non-singular and singular black holes, boson stars and naked singularities, from various theories of gravity. Finally, we provide in a tabular form the first 11 coefficients of the fourth-order RZ parameterization needed to describe a variety of commonly used black-hole spacetimes. When comparing with the first-order RZ parameterization of astrophysical observables such as the ISCO frequency, the coefficients provided here increase the accuracy of two orders of magnitude or more.
