Distant-endpoint approximation

Distant-endpoint asymptote of the first-order weak-field result, ρ₁,ρ₂≫b. Final (2.57) is the exact identity between endpoint logarithm arguments.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 2

ASD-WEB-GRV-022

\Delta T\simeq\frac{2G_0M}{c^3}\ln\!\left(\frac{4\rho_1\rho_2}{b^2}\right)

Distant-endpoint asymptote of the first-order weak-field result, ρ₁,ρ₂≫b. Final (2.57) is the exact identity between endpoint logarithm arguments.
Chapter reference: Final collected manuscript · Chapter 2 §IV.6 (2.58) and the following distant-endpoint asymptote; not final equation (2.57) · ASD-BOOK-ddbade997b45

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Final collected manuscript · Chapter 2 §IV.6 (2.58) and the following distant-endpoint asymptote; not final equation (2.57)

Distant-endpoint asymptote of the first-order weak-field result, ρ₁,ρ₂≫b. Final (2.57) is the exact identity between endpoint logarithm arguments.

Conditions retained in this adoption

Fixed G₀; isolated, static, spherically symmetric, uncharged exterior.
Areal radius, actual spatial length and reference optical path are defined separately.
Weak-field perturbation, slow-rotation far field and boundary statistics each have separate conditions.

Specific unresolved source issues

Microscopic source matching, dynamical strong fields and full boundary-state dynamics remain open.

Source locators: p0759 · p0761 · p0763 · p0765 · p0769 · p0771 · p0773 · p0775 · p0776 · p0779 · 最终合订稿 · 第二章 §四.6 (2.58)后远端点渐近式；不是最终式(2.57)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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FND-3dde8d8e081d · 第二章 / Chapter 2 · (2.57), p. 16

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