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

Saeed Noori Gashti, Mohammad Ali S. Afshar+4 more|arXiv (Cornell University)|Oct 3, 2024

Black Holes and Theoretical Physics5 citations

TL;DR

The paper analyzes the topological charges and photon sphere conditions for Kiselev-AdS black holes in f(R,T) gravity using Duan’s phi-mapping, revealing how the Kiselev parameter omega and gravity parameter gamma affect topological classifications and black hole structure.

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 \(ϕ\)-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 \(ω\) and the \(f(R, T)\) gravity parameter \(γ\) 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 \(ω= 1/3\), in other cases, increasing the parameter \(γ\) increases the number of total topological charges for the black hole. Interestingly, for the phantom field (\(ω= -4/3\)), we observed that decreasing the parameter \(γ\) 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 \(γ\) and \(ω\) effectively expands the permissible range for \(γ\). In other words, the model can exhibit black hole behavior over a larger domain. Additionally, it is evident that with the stepwise reduction of \(ω\), 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.

Motivation & Objective

• Investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-AdS black holes within f(R,T) gravity.
• Establish topological classifications using Duan’s phi-mapping via temperature and generalized Helmholtz free energy methods.
• Examine how the Kiselev parameter omega and the f(R,T) gravity parameter gamma influence topological charges and photon sphere properties.

Proposed method

• Adopt f(R,T)=R+2f(T) with f(T)=gamma T to obtain static spherically symmetric Kiselev-AdS black hole solutions.
• Compute metric functions, Hawking temperature, and entropy; analyze curvature invariants (R, RμνRμν, RμναβRμναβ) and energy conditions.
• Apply Duan’s phi-mapping topological current theory to both the F-method (generalized Helmholtz free energy) and the T-method (temperature) to determine topological charges and zero points.
• Define generalized Helmholtz free energy F=M−S/τ and construct the phi-vector, locating zeros to extract topological charges.
• Investigate photon spheres by analyzing the topological potential H(r,θ) and derive conditions for photon-sphere radii via zero points of the associated phi components.

Experimental results

Research questions

• RQ1 How do the topological charges and numbers of Kiselev-AdS black holes in f(R,T) gravity depend on omega and gamma?
• RQ2 What are the photon-sphere conditions and how are they topologically classified in this setup?
• RQ3 Do the F-method and T-method yield consistent topological classifications for these black holes?
• RQ4 How do curvature invariants and energy conditions behave in relation to the topological structures?
• RQ5 Under what parameter ranges do singularities or horizons persist or vanish?

Key findings

• Total topological charge for the F-method is Q_total = -1 under the considered parameter choices.
• Total topological number for the generalized Helmholtz free energy method is W = +1.
• Oscillations in gamma can increase the number of topological charges for certain omega values, with gamma variations affecting the count of charges.
• For the photon sphere analysis, the study shows that the simultaneous presence of gamma and omega expands the permissible gamma range for black-hole behavior.
• In the photon-sphere case, there exist regions with stable/unstable photon spheres and scenarios without horizons (naked singularities) depending on parameter choices.
• Energy conditions (WEC, NEC, SEC) are satisfied or violated depending on omega and gamma, with SEC largely satisfied for omega<1/3 and gamma>0.