General parametrization of axisymmetric black holes in metric theories of gravity
General parametrization of axisymmetric black holes in metric theories of gravity
复制标题
DOI：
10.1103/physrevd.93.064015
复制
发表时间：
2016-02
影响因子：
5
通讯作者：
R. Konoplya;L. Rezzolla;A. Zhidenko
中科院分区：
文献类型：
--
作者：
R. Konoplya;L. Rezzolla;A. Zhidenko
根据我们以前在球对称性方面的工作，我们在这里提出了一个新的参数框架来描述一般度量引力理论中的轴对称黑洞的时空。在这种情况下，度量分量是径向和极角坐标的函数，迫使双重展开以获得通用轴对称表达式。特别是，我们使用一个连续的分数展开在一个紧凑的径向坐标表示的径向依赖，而我们利用泰勒展开的余弦的极角的极依赖。这些选择导致径向方向上的上级收敛和赤道平面上的精确极限。作为我们的方法的验证，我们建立参数化表示的克尔，旋转介子，爱因斯坦-爱因斯坦-高斯-邦尼特黑洞。在资料片的最低阶，匹配已经很好了，随着新阶的增加，匹配也会提高。我们期望任何静止和轴对称黑洞度规都有类似的行为。
Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.