Thermodynamic topology of black holes in F(R)-Euler–Heisenberg gravity’s Rainbow
Bibliographic record
Abstract
The topology of black hole thermodynamics is a fascinating area of study that explores the connections between thermodynamic properties and topological features of black holes. It often involves analyzing critical points in the phase diagrams of black holes and assigning topological charges to these points. One significant approach is based on Duan’s topological current [Formula: see text]-mapping theory, which introduces the concept of topological charges to critical points in black hole thermodynamics. We successfully derive the field equations for [Formula: see text]-Euler–Heisenberg theory, providing a framework for studying the interplay between modified gravity and nonlinear electromagnetic effects. We obtain an analytical solution for a static, spherically symmetric, energy-dependent black hole with constant scalar curvature. Also, our analysis of black holes in F(R)-Euler–Heisenberg gravity’s Rainbow reveals significant insights into their topological properties. We identified the total topological charges by examining the normalized field lines along various free parameters. Our findings indicate that the parameters [Formula: see text] and [Formula: see text] influence the topological charges. These results are comprehensively summarized in Tables. In examining the photon sphere within this model, the sign of the parameter [Formula: see text] plays a crucial role in determining whether the model adopts a dS or AdS configuration. An interesting characteristic of this model is that, in its AdS form, it avoids the formation of naked singularity regions, which sets it apart from many other models. Typically, varying parameter values in other models can result in the division of space into regions of black holes and naked singularities. However, this model consistently retains its black hole behavior by featuring an unstable photon sphere, regardless of parameter values within the acceptable range. In its dS form, the behavior of the model’s photon sphere remains consistent with other dS models and does not exhibit unique differences.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".