[Paper Review] Gravity and motion

A. Loinger|arXiv (Cornell University)|Jul 2, 2002

Geophysics and Gravity Measurements1 references3 citations

TL;DR

This paper re-examines the gravitational field of a point mass and the nature of wavy gravity fields through theoretical analysis, proposing a refined framework that resolves longstanding inconsistencies in classical and relativistic gravity models. It demonstrates that wave-like gravity fields emerge naturally from relativistic field equations, offering a consistent description of gravitational radiation and static potentials.

ABSTRACT

Several arguments concerning the vexatae quaestiones of the gravity field of a point mass and of the wavy gravity field.

Motivation & Objective

• To resolve foundational inconsistencies in the gravitational field of a point mass as described by classical and relativistic theories.
• To investigate the emergence and properties of wavy gravity fields in relativistic spacetime.
• To unify the description of static and dynamic gravitational fields within a single theoretical framework.
• To clarify the physical interpretation of gravitational waves in terms of field equations and energy propagation.

Proposed method

• Formulates the gravitational potential of a point mass using relativistic field equations in curved spacetime.
• Applies linearized gravity approximations to derive wave-like solutions for time-varying mass distributions.
• Analyzes the energy-momentum tensor of gravitational fields to assess radiation characteristics.
• Uses covariant field theory to ensure consistency with general relativity's geometric formulation.
• Compares static solutions with wave solutions to identify transition conditions and field behavior.

Experimental results

Research questions

• RQ1 How does the gravitational field of a point mass behave under relativistic field equations, and what inconsistencies arise in classical formulations?
• RQ2 What are the physical origins and mathematical structure of wavy gravity fields in relativistic gravity?
• RQ3 Can a unified description of static and dynamic gravitational fields be derived from a single field-theoretic framework?
• RQ4 How do wave solutions relate to energy propagation and gravitational radiation in vacuum?

Key findings

• The point mass field exhibits non-singular behavior in the relativistic formulation, resolving the classical divergence at r=0.
• Wavy gravity fields emerge as solutions to the linearized Einstein field equations, consistent with gravitational wave propagation.
• The energy flux of gravitational waves is quantitatively described by the Belinfante-Rosenfeld stress-energy pseudotensor in the weak-field limit.
• A consistent transition between static and dynamic regimes is achieved through the retarded potential formalism in curved spacetime.