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Title Topological Classes of Stationary Axisymmetric Black Holes

Author(s) Haseeb Nazar

Abstract In recent years, the study of black holes has gained significant attention, particularly in the context of their topological properties. In this thesis, we investigate the topological numbers of Kiselev black holes, rotating Kiselev black holes, Kerr-Newman black holes, and Kerr-AdS black holes in the presence of a quintessential field. Our primary focus is to analyze whether the quintessential field influences the topological number of these black holes. We classify the black holes into three topological classes based on the topological: −1, 0, and 1. Through our analysis, we find that the presence of the quintessential field does not affect the topological number of these black holes. Additionally, in the case of Kerr-Ads black holes, we observe the presence of an annihilation point. To further investigate the impact of the quintessential field, we explore the effect of the state parameter ω within the interval −1 < ω < −1/3 by selecting different values. Our results indicate that while the curves exhibit slight deviations, the winding number and topological number remain unchanged. Similarly, we analyze the impact of varying the quintessential parameter c and find that it does not alter the topological number of black holes. These findings suggest that the quintessential field does not play a role in modifying the topological nature of black holes. Since topological numbers are crucial in understanding black hole thermodynamics, our study provides valuable insights into the stability and classification of black holes in the presence of exotic fields.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2025-07-18

Subject Mathematics

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