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Geodesic flows in rotating black hole backgrounds

Anirvan Dasgupta*

Hemwati Nandan†

Sayan Kar‡

  • Department of Mechanical Engineering and Centre for Theoretical Studies Indian Institute of Technology, Kharagpur 721 302, India

  • Department of Physics Gurukula Kangri Vishwavidyalaya, Haridwar 249 404, Uttarakhand, India

  • Department of Physics and Centre for Theoretical Studies Indian Institute of Technology, Kharagpur 721 302, India

  • *anir@mech.iitkgp.ernet.in
  • †hntheory@yahoo.co.in
  • ‡sayan@iitkgp.ac.in
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Phys. Rev. D 85, 104037 – Published 23 May, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.104037

Abstract

We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three [the Bañados-Teitelboim-Zanelli (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 Bañados-Teitelboim-Zanelli case, the equations are solved analytically. The effect of the negative cosmological constant on the evolution of the expansion (θ), for congruences with and without an initial rotation (ω0), 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 ω0. Further, the role of a and ω0 on the time (affine parameter) of approach to singularity (defocusing/focusing) is studied. While the role of ω0 on the time to singularity is as expected, the effect of a leads to an interesting new result.

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See Also

Kinematics of geodesic flows in stringy black hole backgrounds

Anirvan Dasgupta, Hemwati Nandan, and Sayan Kar
Phys. Rev. D 79, 124004 (2009)

Article Text

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Outline

Information

Phys. Rev. D 85, 104037– Published 23 May, 2012
  • Received 29 February 2012

© 2012 American Physical Society

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