Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-02-24
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Sixteen pages, five figures
Scientific paper
We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three (the BTZ) and four (the Kerr) dimensions. The evolution (Raychaudhuri) equations for the expansion, shear and rotation along geodesic flows in such spacetimes are obtained. For the BTZ case, the equations are solved analytically. The effect of the negative cosmological constant on the evolution of the expansion ($\theta$), for congruences with and without an initial rotation ($\omega_0$) is noted. Subsequently, the evolution equations, in the case of a Kerr black hole in four dimensions are written and solved numerically, for some specific geodesics flows. It turns out that, for the Kerr black hole, there exists a critical value of the initial expansion below (above) which we have focusing (defocusing). We delineate the dependencies of the expansion, on the black hole angular momentum parameter, $a$, as well as on $\omega_0$. Further, the role of $a$ and $\omega_0$ on the time (affine parameter) of approach to a singularity (defocusing/focusing) is studied. While the role of $\omega_0$ on this time of approach is as expected, the effect of $a$ leads to an interesting new result.
DasGupta Anirvan
Kar Sayan
Nandan Hemwati
No associations
LandOfFree
Geodesic flows in rotating black hole backgrounds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geodesic flows in rotating black hole backgrounds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesic flows in rotating black hole backgrounds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-78180