Ricci and Weyl curvature

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

Ricci and Weyl curvature are distinguished in the manuscript’s correction of an argument about mass and spacetime. Stress-energy sources the Ricci curvature described by Einstein’s equations, while a surrounding Ricci-flat vacuum can still possess nonzero Weyl curvature carrying tidal and propagating gravitational structure. Ricci-flat therefore does not mean flat, and ordinary general relativity does not establish that curvature vanishes wherever matter is present.

Explanation

The distinction is introduced to reject an attempted justification of the claim that mass lies outside spacetime. The rejected inference would require curvature to vanish at mass. RB1 instead states that nonvanishing stress-energy sources Ricci curvature there and distinguishes that situation from the surrounding vacuum’s remaining Weyl curvature.

This is a correction within the author’s presentation, not a new derivation of all curvature decompositions in every gravitational model. The native note identifies the source route through Carroll and Bertschinger. The proposed entry preserves that extent and does not silently turn a popular rubber-sheet image into a general-relativistic theorem.

The stronger mass-substratum idea remains internal to the speculative transactional-gravity program. RB2 explicitly says measurable curvature is not absent at mass, while RB1 carries forward a weaker priority claim as interpretation. Distinguishing Ricci and Weyl prevents that conjecture from borrowing authority from a physical argument the manuscript itself refuses.

Scope and attribution

Bound the entry to the manuscript’s stated correction and preserve the conjecture’s separate status.

RB1 — The Real Book, Volume I: The Possible Is Real

The Ricci-Weyl distinction corrects a rejected curvature-at-mass inference, with native references retained.

Occurrence locators: 93.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.