Thermodynamic Topology of Kiselev-AdS Black Holes within f (R, T) gravity

TL;DR

This paper explores the topological properties of Kiselev-AdS black holes in f(R, T) gravity, revealing how parameters influence topological charges and photon sphere conditions, and expanding the understanding of black hole classifications.

Contribution

It introduces a novel topological classification of Kiselev-AdS black holes within f(R, T) gravity using two different methods, highlighting the effects of specific parameters on topological charges.

Findings

Topological charges depend on mega and b; parameters influence black hole classification.

Total topological charge is -1 and total topological number is +1 for the studied models.

Parameter variations expand the permissible range for black hole behavior and affect the photon sphere conditions.

Abstract

In this paper, we investigate the topological charge and the conditions for the existence of the photon sphere (PS) in Kiselev-AdS black holes within \(f(R, T)\) gravity. We employ two different methods based on Duan's topological current \(\phi\)-mapping theory viz analize of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole. By considering the mentioned black hole, we discuss the critical and zero points (topological charges and topological numbers) for different parameters. Our findings reveal that the Kiselev parameter \(\omega\) and the \(f(R, T)\) gravity parameter \(\gamma\) influence the number of topological charges of black holes, leading to novel insights into topological classifications. We observe that for given values of the free parameters, there exist total topological charges (\(Q_{total} = -1\)) for T-method and total topological numbers (\(W = +1\)) for the generalized Helmholtz free energy method. Our research findings elucidate that, in contrast to the scenario where \(\omega = 1/3\), in other cases, increasing the parameter \(\gamma\) increases the number of total topological charges for the black hole. Interestingly, for the phantom field (\(\omega = -4/3\)), we observed that decreasing the parameter \(\gamma\) increases the number of topological charges. Additionally, we study the results for the photon sphere. The studied models clearly reveal that the simultaneous presence of \(\gamma\) and \(\omega\) effectively expands the permissible range for \(\gamma\). In other words, the model can exhibit black hole behavior over a larger domain. Additionally, it is evident that with the stepwise reduction of \(\omega\), the region covered by singularity also diminishes and becomes more restricted. However, An interesting point about all three ranges is the elimination of the forbidden region in this model.