Head-on collision of ultrarelativistic particles in ghost-free theories of gravity
Bibliographic record
Abstract
We study linearized equations of a ghost-free gravity in four- and higher-dimensional spacetimes. We consider versions of such a theory where the nonlocal modification of the $\ensuremath{\square}$ operator has the form $\ensuremath{\square}\mathrm{exp}[(\ensuremath{-}\ensuremath{\square}/{\ensuremath{\mu}}^{2}{)}^{N}]$, where $N=1$ or $N=2n$. We first obtain the Newtonian gravitational potential for a point mass for such models and demonstrate that it is finite and regular in any number of spatial dimensions $d\ensuremath{\ge}3$. The second result of the paper is calculation of the gravitational field of an ultrarelativistic particle in such theories. And finally, we study a head-on collision of two ultrarelativistic particles. We formulated conditions of the apparent horizon formation and showed that there exists a mass gap for mini-black-hole production in the ghost-free theory of gravity. In the case when the center-of-mass energy is sufficient for the formation of the apparent horizon, the latter has two branches, the outer and the inner ones. When the energy increases the outer horizon tends to the Schwarzschild-Tangherlini limit, while the inner horizon becomes closer to $r=0$.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 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".