Hidden conformal symmetry of the Kerr black hole
Why this work is in the frame
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Bibliographic record
Abstract
Extreme and very-near-extreme spin $J$ Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges ${c}_{L}={c}_{R}=12J$. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass $M\ensuremath{\ne}\sqrt{J}$. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The $2\ensuremath{\pi}$ periodic identification of the azimuthal angle $\ensuremath{\phi}$ is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures ${T}_{L}={M}^{2}/2\ensuremath{\pi}J$ and ${T}_{R}=\sqrt{{M}^{4}\ensuremath{-}{J}^{2}}/2\ensuremath{\pi}J$. The well-known low-frequency scalar-Kerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the Bekenstein-Hawking area law for all $M$ and $J$. These observations provide evidence for the conjecture that the Kerr black hole is dual to a ${c}_{L}={c}_{R}=12J$ 2D CFT at temperatures (${T}_{L},{T}_{R}$) for every value of $M$ and $J$.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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