论文标题
Kerr Spacetime的基本轨道频率的重力校正
Modified Gravity Corrections in Fundamental Orbital Frequencies in Kerr Spacetime
论文作者
论文摘要
作为对修饰的重力理论的极限比率的计算波形的第一步，我们计算了一个小型紧凑型物体的轨道频率灵感到超大的黑洞，以用于非局部重力模型。小型紧凑型物体沿轨道移动，该轨道可以将其近似于背景时空的大地测量，这是由于中央黑洞与小紧凑型物体的质量大比。总体而言，基本轨道频率$ω_r，\;ω_θ$和$ω_DISCON可以通过求解Kerr Metric的Geodesic方程来计算。如果我们将任何修改的重力理论作为一般相对论的较小校正，那么该理论中旋转黑洞周围的时空度量可以被视为具有较小变形的Kerr公制。这将使我们能够计算轨道对象的大地运动的基本频率，即作为Kerr频率加上来自修饰的重力部分的Kerr频率的少量偏移。使用动作角度形式主义和规范的扰动理论，I计算了围绕旋转黑洞的轨道运动的KERR频率，用于非局部重力理论的RR模型。
As a first step towards the calculation of waveform of Extreme Mass Ratio Inspirals for Modified Gravity theories, we calculate the orbital frequencies of a Small Compact Object inspiralling into a super massive blackhole for a Nonlocal gravity model. The small compact object moves along an orbit which can be approximated to a geodesic of the background spacetime due to large mass ratio of central blackhole to Small Compact Object. In General Relativity, the fundamental orbital frequencies $Ω_r,\;Ω_θ$ and $Ω_ϕ$ can be calculated by solving geodesic equations of the Kerr metric. If we formulate any modified gravity theory as a small correction in General Relativity then the spacetime metric around a rotating blackhole in that theory can be considered as the Kerr metric with small deformations. This would allow us to calculate fundamental frequencies of geodetic motion of the orbiting object perturbatively i.e. as Kerr frequencies plus small shifts in Kerr frequencies coming from the modified gravity part. Using Action-angle formalism and canonical perturbation theory I calculate the frequency shifts with respect to Kerr frequencies of the orbital motion around a rotating blackhole for RR model of Nonlocal gravity theory.
