[Paper Review] Gravitomagnetic forces and quadrupole gravitational radiation from special relativity

P. Christillin, Lorenzo Barattini|arXiv (Cornell University)|Feb 13, 2012

Cosmology and Gravitation Theories8 references3 citations

TL;DR

This paper derives gravitomagnetic forces and quadrupole gravitational radiation from special relativity alone, without assuming general relativity. By applying Lorentz transformations to mass currents with a factor-of-2 correction due to relativistic mass variation, it predicts gravitational radiation at speed c with energy flux matching general relativity, offering a parameter-free, flat-space explanation of gravitational waves via elementary relativistic electromagnetism analogies.

ABSTRACT

The mere principle of relativity and Lorentz transformations for the mass current predict, in close analogy to electromagnetism, the existence of gravitomagnetic fields. With the reasonable assumption of the non existence of a gravitomagnetic mass, a parameter-free set of equations for "effective" vector gravitoelectromagnetism results. As a consequence gravity propagates at the speed of light in a flat Minkowski space and quadrupole gravitational radiation, consistent with energy balance, is predicted with the same value of GR. Heuristic considerations relate gravitational radiation to the strong field parameter $\frac {GM}{c^2 r}$, suggesting the complete evaporation of a black hole at the Planck scale.

Motivation & Objective

• To show that gravitomagnetic effects and quadrupole gravitational radiation can be derived from special relativity alone, without invoking general relativity.
• To resolve inconsistencies in existing gravitoelectromagnetism (GEM) formulations by identifying the correct coefficient for the mass current in the Lorentz force law.
• To demonstrate that the propagation speed of gravity and the quadrupole radiation power are consistent with general relativity when derived from relativistic mass current transformations.
• To argue that the factor of 4 in the quadrupole radiation formula arises naturally from a double relativistic correction (mass and length transformation), not from spacetime curvature or spin-2 gravitons.
• To provide a simpler, parameter-free alternative interpretation of gravitational waves based on special relativity and effective vector fields analogous to electromagnetism.

Proposed method

• Apply Lorentz transformations to a mass current density, accounting for relativistic mass increase, which introduces a factor of 2 difference from electromagnetic current density.
• Use the principle of relativity to derive an effective gravitomagnetic field analogous to the magnetic field in electromagnetism, with the same functional form but with G replacing 1/(4πε₀) and 2m replacing q.
• Construct a parameter-free set of vector equations for gravitoelectromagnetism (GEM) by mimicking Maxwell's equations with the corrected current density and relativistic mass effects.
• Derive the quadrupole gravitational radiation formula by analogy with electromagnetic quadrupole radiation, replacing q → 2m and 1/(4πε₀) → G, yielding the correct GR result.
• Verify consistency by checking that the radiation power matches the general relativity prediction and that the propagation speed is c, avoiding causality violations from incorrect current coefficients.
• Demonstrate that the factor of 4 in the radiation formula arises from the combined effect of two relativistic corrections (mass and length transformation), not from spacetime curvature.

Experimental results

Research questions

• RQ1 Can gravitomagnetic forces and quadrupole gravitational radiation be derived from special relativity without assuming general relativity?
• RQ2 What is the correct coefficient for the mass current in the Lorentz force law when relativistic mass variation is properly accounted for?
• RQ3 Why do existing GEM formulations fail to predict the correct radiation power and propagation speed, and how can they be corrected?
• RQ4 Does the factor of 4 in the quadrupole gravitational radiation formula originate from relativistic mass effects or from spacetime curvature?
• RQ5 Can the observed periastron advance and orbital decay in binary pulsars be explained by a flat-space, special relativity-based model of gravity?

Key findings

• The correct coefficient for the mass current in the gravitomagnetic force law is 2, arising from the relativistic mass increase, not 1 or 4 as in some existing GEM formulations.
• Quadrupole gravitational radiation is derived from special relativity with the same power formula as in general relativity: $ W_G = \frac{G}{45c^5} \left( \frac{d^3Q}{dt^3} \right)^2 $, matching GR predictions exactly.
• The propagation speed of gravitational waves is c in flat Minkowski spacetime, consistent with causality and special relativity.
• The factor of 4 in the radiation formula arises from a double relativistic correction: the 2× increase in mass current and the 2× increase in the effective charge (2m), not from spacetime curvature.
• Incorrect GEM formulations with current coefficient 1, 2, or 4 lead to violations of causality or energy conservation, as they predict radiation powers or speeds inconsistent with GR.
• The periastron precession and orbital decay of binary pulsars can be derived from the same relativistic mass current framework, suggesting that spacetime curvature may be an emergent description rather than fundamental.