Kerr Metric, Geodesic Motion, and Flyby Anomaly in Fourth-Order Conformal Gravity
Gabriele U. Varieschi
备注：
Revised version: improved notation, added references, comments, and one equation. 31 pages, including 2 figures. Accepted for publication in General Relativity and Gravitation
In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity. Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard General Relativity Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton-Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion-similar to Carter's constant-can also be introduced in Conformal Gravity. Consequently, we derive the fundamental equations of geodesic motion and show that the problem of solving these equations can be reduced to one of quadratures. In particular, we study the resulting time-like geodesics in Conformal Gravity Kerr geometry by numerically integrating the equations of motion for Earth flyby trajectories of spacecraft. We then compare our results with the existing data of the Flyby Anomaly in order to ascertain whether Conformal Gravity corrections are possibly the origin of this gravitational anomaly. Although Conformal Gravity slightly affects the trajectories of geodesic motion around a rotating spherical object, we show that these corrections are minimal and are not expected to be the origin of the Flyby Anomaly, unless conformal parameters are drastically different from current estimates. Therefore, our results confirm previous analyses, showing that modifications due to Conformal Gravity are not likely to be detected at the Solar System level, but might affect gravity at the galactic or cosmological scale.
Constructing the canonical harmonic coordinates of Kerr metric to the fourth post-Minkowskian order
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；School of Mathematics and Statistics, and Hunan Provincial University Key Laboratory for Big Data Analysis and Application, Hunan First Normal University（湖南第一师范学院数学与统计学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学科学学院）
Resumming Kerr Quasinormal-Mode Frequencies: Accuracy and Breakdown Near Extremality
Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校宇宙高级研究中心与物理系）；Department of Physics, University of Virginia（弗吉尼亚大学物理系）
