[Paper Review] Gravitatomagnetic Analogs of Electric Transformers

J.D. Swain|arXiv (Cornell University)|Jun 30, 2010

Relativity and Gravitational Theory1 references3 citations

TL;DR

This paper proposes a gravitational analog of an electrical transformer, where time-varying mass-energy currents generate changing gravitomagnetic fields that induce a gravitomotive force in a secondary winding, analogous to electromagnetic induction. The key contribution is the theoretical framework for near-field gravitational induction, enabling new tests of general relativity and searches for gravitomagnetic materials via high-energy particle beams like those at the LHC.

ABSTRACT

Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism has been used to understand gravitomagnetic effects like the Lense-Thirring dragging of inertial frames. For time-varying mass-energy currents, the analog of Faraday's law suggests new effects based on the gravitational equivalent of a transformer where such currents take the place of electrical currents. New experimental possibilities are suggested including a novel coupling mechanism of electromagnetism to gravity, new tests of general relativity in the ultrarelativistic limit using particle beams in the LHC, and searches for a materials exhibiting the gravitational analog of ferromagnetism.

Motivation & Objective

• To establish a theoretical framework for gravitomagnetic induction analogous to electromagnetic transformers in linearized general relativity.
• To explore experimental possibilities for detecting gravitomagnetic effects using high-energy particle beams, particularly at the LHC.
• To propose a novel coupling mechanism between electromagnetism and gravity via time-varying mass currents.
• To investigate the potential existence of materials with gravitational analogs of ferromagnetic properties, such as high gravitomagnetic permeability.
• To distinguish near-field gravitomagnetic induction from gravitational radiation, emphasizing suppression-free effects in relativistic regimes.

Proposed method

• Adopt the linearized gravity formalism with gravitoelectric and gravitomagnetic fields analogous to Maxwell’s equations.
• Define the gravitomotive force 𝒢 as the line integral of the gravitoelectric field, analogous to electromotive force.
• Use the Faraday-like law ∇×E = −(1/c) ∂(½B)/∂t to describe induction from time-varying gravitomagnetic flux.
• Model the primary winding as a time-varying mass-energy current, such as a pulsed beam of relativistic particles in the LHC.
• Apply the equation 𝒢 = −(2/c) d/dt ∫B·da to compute the induced gravitomotive force in the secondary winding.
• Propose using superconducting or superfluid materials as secondary windings to minimize losses and enhance sensitivity to gravitomagnetic effects.

Experimental results

Research questions

• RQ1 Can a gravitational transformer be constructed using time-varying mass-energy currents instead of electrical currents?
• RQ2 What are the experimental signatures of near-field gravitomagnetic induction in high-energy particle accelerators like the LHC?
• RQ3 Is there a gravitational analog of ferromagnetism, and can it be detected via a transformer-like setup?
• RQ4 How does gravitomagnetic induction differ from gravitational wave radiation in terms of field behavior and detectability?
• RQ5 Can electromagnetic forces drive mass currents that simultaneously generate measurable gravitomagnetic fields and induce gravitomotive forces in a secondary loop?

Key findings

• The paper establishes that a gravitational transformer can be realized in linearized general relativity, where time-varying mass-energy currents induce a gravitomotive force in a secondary winding via changing gravitomagnetic flux.
• The induced gravitomotive force is given by 𝒢 = −(2/c) d/dt ∫B·da, analogous to Faraday’s law in electromagnetism.
• High-energy particle beams at the LHC, such as 7 TeV protons with γ ≈ 7000, provide a viable platform for observing near-field gravitomagnetic induction due to high rates of change of flux and suppressed v/c suppressions.
• The effect is strictly near-field and distinct from gravitational radiation, avoiding retardation and v/c suppression, making it more detectable than gravitational wave emission.
• The use of superconducting or superfluid materials as secondary windings could enhance sensitivity and allow detection of the gravitational analog of magnetic permeability.
• The paper suggests that ferromagnetic-like materials may exist in gravity, and their search could be enabled by such a transformer setup, despite no current theoretical prediction of their existence.