Arnold diffusion and geodesic dynamics of blackholes

KAM and geodesic dynamics of blackholes

In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply mainly to two observable phenomena: the photon shell (unstable bound spherical orbits) and the quasi-periodic oscillations. We discover there is a gap structure in the photon shell that can be used to reveal information of the perturbation.

Geodesic Motion in a Charged 2D Stringy Blackhole Spacetime

We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacet…

Modified Gravity Corrections in Fundamental Orbital Frequencies in Kerr Spacetime

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…

Optical 2-metrics of Schwarzschild-Tangherlini Spacetimes and the Bohlin-Arnold Duality

We consider the projection of null geodesics of the Schwarzschild-Tangherlini metric in n+1 dimensions to the space of orbits of the static Killing vector where the motion of a given light ray is seen to lie in a plane. The projected curves coincide with the unparametrised geodesics of optical 2-metrics and can be equally understood as describing the motion of a non-relativistic particle in a central force. We consider a duality between the projected null curves for pairs of values of n and interpret its mathematical meaning in terms of the optical 2-metrics. The metrics are not projectively e…

渐近平坦规则黑洞在幻影狄拉克-玻恩-因费尔德引力中的Eikonal振铃、阴影、透镜、灰体因子和结合能

Eikonal Ringing, Shadows, Lensing, Grey-Body Factors, and Binding Energy of Asymptotically Flat Regular Black Holes in Phantom Dirac-Born-Infeld Gravity

本文利用测地线光学方法研究了幻影DBI引力中规则黑洞的eikonal准正规振荡、阴影、强透镜、灰体因子和结合能，发现所有可观测量由单个无量纲函数决定。

耦合常数变态、费马原理与Kerr度规中的光传播

Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric

本文利用耦合常数变态简化Kerr度规中基于费马原理的测地线哈密顿量，将其化为动量二次型并依赖初始能量，从而便于直接积分或微扰处理，并推广至五维Myers–Perry度规的单旋转参数情形。