Generalized quasi-topological gravities: the whole shebang
Bibliographic record
Abstract
Abstract Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity in D -dimensions. Their defining properties include possessing second-order linearized equations of motion around maximally symmetric backgrounds as well as non-hairy generalizations of Schwarzschild’s black hole characterized by a single function, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≡</mml:mo> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>r</mml:mi> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , which satisfies a second-order differential equation. In (Bueno et al 2020 Class. Quantum Grav. 37 015002) GQTGs were shown to exist at all orders in curvature and for general D . In this paper we prove that, in fact, n − 1 inequivalent classes (as far as static and spherically symmetric solutions are concerned) of order- n GQTGs exist for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> . Amongst these, we show that one—and only one—type of densities is of the quasi-topological kind, namely, such that the equation for f ( r ) is algebraic. Our arguments do not work for D = 4, in which case there seems to be a single unique GQT density at each order which is not of the quasi-topological kind. We compute the thermodynamic charges of the most general D -dimensional order- n GQTG, verify that they satisfy the first law and provide evidence that they can be entirely written in terms of the embedding function which determines the maximally symmetric vacua of the theory.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".