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This study aims to derive the geometric response of spacetime to localized scalar sources in a weak-field framework of general relativity.

May 31, 20260 citationsOpen Access

Scaling Structure of Geometric Backreaction from Localized Scalar Sources in a Controlled Weak-Field Gravitational Expansion

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NTNGUYEN DUC TAI

Key Points

This study aims to derive the geometric response of spacetime to localized scalar sources in a weak-field framework of general relativity.
Developed a weak-field gravitational expansion using dimensionless coupling.
Solved the Einstein equations for a static, spherically symmetric spacetime.
Obtained analytic expressions for the shape and redshift functions.
Generated closed-form solutions for the shape function b(r) and the redshift function Φ(r).
Demonstrated the leading-order geometric response dependent on scalar source parameters.

Abstract

We derive the complete leading-order geometric response of a static, spherically symmetric spacetime to a localized, minimally coupled massless scalar source within a rigorously controlled weak-field expansion of general relativity. Working at first order in the small coupling ϵ = 16πGs2 0 (dimensionless in natural units), we solve both independent Einstein equations and obtain closed form analytic expressions for the shape function b(r) and the redshift function Φ(r) in terms of the lower incomplete gamma function γ...

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Scaling Structure of Geometric Backreaction from Localized Scalar Sources in a Controlled Weak-Field Gravitational Expansion

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