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June 28, 20260 citationsOpen Access

Motti Intermediate Physics - HAL: The Fold Operator as a Smoothed BMS Generator - A Formal Proof via Two Lemmas

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MAMordecai Gavila AlvarezValencia Catholic University Saint Vincent Martyr

Key Points

  • This research aims to prove that the HAL fold operator generates smoothed BMS supertranslations on S2.
  • Formal proof via two lemmas
  • Analysis of the relation between the fold operator and angular operator
  • Application of Bondi equations for observable modes.
  • P-hat operator is shown to be equal to (1-alpha2 nabla_S2)^{-1} Q_BMS_GR
  • Observable modes l less than 10 exhibit below 1.3 percent deviation
  • Closure of Strominger triangle verified with C0 factor.

Abstract

Formal proof that the HAL fold operator P-hat generates smoothed BMS supertranslations on S2. Lemma 1: P-hat, d/du = 0 (purely angular operator). Lemma 2: dᵤ C0 = -kappa P-hat C0 (Bondi EOM). Theorem: P-hat = (1-alpha2 nablaS2) ^-1 QBMSGR. Observable modes l less than 10: below 1. 3 percent deviation. Task 2 Step 4 closed. Strominger triangle closes with C0 factor.

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Cite This Study

Mordecai Gavila Alvarez (2026) studied this question.

synapsesocial.com/papers/6a40b9f361bb0a67205c6012https://doi.org/10.5281/zenodo.20937074
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