Derivation of general relativistic gravitational potential energy using principle of equivalence and gravitational time dilation
Bibliographic record
Abstract
Einstein’s theory of general relativity, which has been experimentally proved to be a true theory of gravity does not need gravitational potential energy to predict the trajectory of particles in space. This is because general relativity is a purely geometric theory. Objects move along the geodesics in the curved space–time. The energy–momentum tensor that warps space–time as per Einstein’s field equations takes into account only the energy–momentum of matter and radiation. Thus, gravitational potential energy does not come into the picture in Einstein’s theory of gravity and its role is taken over by the curvature of space–time. However, a general relativistically correct expression for gravitational potential energy is required for energy conservation and some energy-based approaches in physics. Conventionally, the correct form of gravitational potential energy is derived by using the full mathematical formality of general relativity. In this paper, we derive the same general relativistic expression for gravitational potential energy simply by using the principle of equivalence and gravitational time dilation.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".