[Paper Review] Exact 'antigravity-field' solutions of Einstein's equation

F. S. Felber|ArXiv.org|Mar 19, 2008

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper derives exact time-dependent solutions of Einstein's field equations for a relativistically moving spherical mass, demonstrating that such objects can generate repulsive 'antigravity' fields under specific conditions. The key result shows that particles at rest experience gravitational repulsion when the source mass exceeds a velocity-dependent threshold, with field strength and position determining the onset of antigravity effects.

ABSTRACT

Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of particles at rest are determined as a function of source speed and field strength and particle position.

Motivation & Objective

• To derive exact solutions of Einstein's gravitational field equations for a mass moving at relativistic speeds.
• To determine the conditions under which such a moving mass generates a repulsive (antigravity) field for stationary test particles.
• To establish the relationship between source velocity, field strength, and particle position in enabling gravitational repulsion.
• To validate the exact antigravity field solution against weak-field approximations using retarded potentials.

Proposed method

• The study employs a metric first derived by Hartle, Thorne, and Price to model the gravitational field of a relativistically moving spherical mass.
• It applies exact solutions of Einstein's field equations to analyze the time-dependent gravitational field of the moving mass.
• The paper compares the exact antigravity field with weak-field approximations derived from retarded potentials to confirm consistency.
• It calculates the impulse imparted to a test particle by the antigravity field, providing a dynamical measure of the repulsive effect.
• The analysis incorporates the dependence of field strength on the source's velocity and the spatial position of the test particle.
• The solution is validated through correspondence with prior weak-field results, confirming the physical relevance of the exact field.

Experimental results

Research questions

• RQ1 Under what conditions does a relativistically moving mass generate a repulsive gravitational field for a stationary test particle?
• RQ2 How does the threshold velocity for antigravity depend on the field strength and particle position relative to the source?
• RQ3 What is the quantitative correspondence between the exact antigravity field and weak-field approximations based on retarded potentials?
• RQ4 How is the impulse transferred to a test particle by the antigravity field, and what does this imply for momentum conservation?
• RQ5 Can the exact solution be consistently matched with known results from linearized gravity in the weak-field limit?

Key findings

• The exact solution confirms that a relativistically moving spherical mass can generate a repulsive gravitational field for stationary test particles.
• Gravitational repulsion occurs when the source mass exceeds a velocity threshold that depends on the field strength and the particle's position.
• The threshold condition for antigravity is derived as a function of source speed and field strength, with higher speeds enabling repulsion at greater distances.
• The exact antigravity field matches weak-field approximations based on retarded potentials, validating the solution's consistency with established electromagnetic analogs.
• The impulse imparted to a test particle by the antigravity field is calculated, showing a measurable momentum transfer consistent with relativistic energy-momentum conservation.
• The results demonstrate that the antigravity effect is not an artifact of approximation but a real feature of general relativity under specific dynamical conditions.