Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics
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Bibliographic record
Abstract
A bstract This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity, focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles with a star product structure determined by R-flux deformations in string theory. For the nonassociative vacuum Einstein equations we consider both real and complex effective sources. In order to analyze the nonassociative vacuum Einstein equations we develop the anholonomic frame and connection deformation methods, which allows one to decoupled and solve these equations. The metric coefficients can depend on both space-time coordinates and energy-momentum. By imposing conditions on the integration functions and effective sources we find physically important, exact solutions: (1) 6-d Tangherlini BHs, which are star product and R-flux distorted to 8-d black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE configurations generalizing Schwarzschild-de Sitter metrics. We also investigate the concept of Bekenstein-Hawking entropy and find it applicable only for very special classes of nonassociative BHs with conventional horizons and (anti) de Sitter configurations. Finally, we show how analogs of the relativistic Perelman W-entropy and related geometric thermodynamic variables can be defined and computed for general classes of off-diagonal solutions with nonassociative R-flux deformations.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it