Thermodynamic geometric analysis of RN black holes under <i>f</i> ( <i>R</i> ) gravity
Bibliographic record
Abstract
This paper investigates the thermodynamic phase structure and microscopic interactions of Reissner–Nordström (RN) black holes within the framework of f( R) gravity. The academic rationale is to explore how modifications to Einstein’s gravity influence the critical behavior of charged black holes. We employ the tools of thermodynamic geometry, specifically the Ruppeiner curvature, to probe the nature of interactions among the black hole’s microscopic constituents. Our analysis reveals that the thermodynamic behavior is highly sensitive to the functional form of f( R) and the background space–time geometry. For models with a constant initial curvature scalar, RN black holes exhibit thermodynamic properties analogous to an ideal gas. However, for models where the initial curvature scalar is non-constant, corresponding to a cosmological constant with negative power terms, we uncover a first-order phase transition analogous to that of a Van der Waals fluid. This transition is characterized by the canonical “swallowtail” catastrophe in the Gibbs free energy landscape. The divergence of the Ruppeiner curvature scalar is shown to precisely coincide with the critical points of this phase transition, providing a geometric signature of the underlying change in the black hole’s microstructure. Our results demonstrate that f( R) gravity parameters and background topology are critical determinants of black hole stability, offering a new window into the phenomenological consequences of modified gravity theories.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".