Thermodynamic topology of Kiselev-AdS black holes within f (R, T) gravity
Bibliographic record
Abstract
Abstract In this paper, we investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-anti-de Sitter (AdS) black holes within gravity. Furthermore, we establish their topological classifications. We employ two different methods based on Duan’s topological current ϕ -mapping theory viz analysis of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole. Considering this 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 gravity parameter γ influence the number of topological charges of black holes, providing novel insights into topological classifications. We observe that for given values of the free parameters, total topological charges ( ) exist for the T method and total topological numbers ( ) for the generalized Helmholtz free energy method. Our research findings elucidate that, in contrast to the scenario in which , in other cases, increasing γ increases the number of total topological charges for the black hole. Interestingly, for the phantom field ( ), we observe that decreasing γ increases the number of topological charges. Additionally, we study the results for the photon sphere. The studied models 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, we observe that with the stepwise reduction of ω , the region covered by singularity diminishes and becomes more restricted. However, an interesting point about all three ranges is the elimination of the forbidden region in this model. In other words, this model and the investigated areas appear to have no region in which both the ϕ and metric functions simultaneously lack solutions. Additionally, we fully check the curvatures singularities and energy conditions for the mentioned black hole.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".