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Title TOPOLOGY OF EQUATORIAL TIMELIKE CIRCULAR ORBITS AROUND KERR-LIKE BLACK HOLES

Author(s) Fatima Arshad

Abstract A topological approach has been successfully used to study the properties of the light ring and null circular orbit in generic black hole spacetime. In this work, a detailed review of the general framework is extended to investigate the topology of equatorial timelike circular orbits (TCOs) around a generic asymmetric, stationary, asymptotically flat black hole spacetime. The topological analysis of the Kerr black hole and Kerr-like black holes in a perfect fluid dark matter (PFDM) background is conducted. It is found that the dynamics of test particles affected by the gravitational field of the black hole are examined using a unique topological framework developed for generic axisymmetric stationary, asymptotically flat black holes. Furthermore, when the angular momentum is held constant, there are two possibilities: 1) the absence of timelike circular orbits, or 2) the presence of TCOs occurring in pairs, with one stable and one unstable. Additionally, the stable and unstable timelike circular orbits have positive and negative winding numbers, respectively, and the radii of these circular orbits correspond to the zero points of the constructed n vector field. Similar results are observed for black holes in a PFDM background. However, for any fixed value of the particle parameter, the presence of PFDM increases the radius of TCOs.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2024-12-06

Subject Mathematics

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