BH2 - Theoretical and observational studies of astrophysical black holes |
|
Speaker |
Rana, Prerna |
|
Coauthors |
Mangalam, A. |
| Talk Title |
Alternate Forms For Trajectories of Bound Orbits in Kerr Geometry |
|
Abstract |
We derive new closed form analytic solutions for general non-equatorial eccentric bound trajectories, $\{ \phi \left( r, \theta \right)$, $\ t \left( r, \theta \right),\ r \left( \theta \right) \}$, around a Kerr black hole by using the transformation $1/r=\mu \left(1+ e \cos \chi \right)$. We obtain and implement translation relations between energy and angular momentum of the particle, ($E$, $L$), and eccentricity and inverse-latus rectum, ($e$, $\mu$), for a given spin, $a$, and $Q$ to obtain the trajectory completely in the ($e$, $\mu$, $a$, $Q$) parameter space. The solutions for the specific case of non-equatorial separatrix orbits uses the $\chi$ variable, which has direct applications to gravitational wave astronomy. Using long time averages, we derive the novel closed form expressions of the fundamental frequencies of non-equatorial eccentric trajectories, ($\nu_{\phi}$, $\nu_{\theta}$, $\nu_{r}$). We discuss simple reduced formulae for non-equatorial eccentric, non-equatorial separatrix, zoom whirl, spherical orbits, and their importance in selected astrophysical applications. |
|
Talk view |
|
|
|
|