1. Field Energy in GEM Field Theory
W. J. Wilson
Department of Engineering and Physics
University of Central Oklahoma
Edmond, OK 73034

2. OAS Fall 2007 Technical Meeting
Outline
The Field Energy Problem of GR
Linearized GR  GEM Theory
Analogy of GEM with Maxwell EM Theory
Gravitational Field Energy in GEM Theory
Gravitational Radiation in GEM Theory
Stability of Gravitational Bound States in GEM
Conclusions
OAS Fall 2007 Technical Meeting

3. The Field Energy Problem of GR
There is no well-defined gravitational field energy in General Relativity (L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Sec. 96)
Standard methods to obtain the energy-momentum tensor in GR do not work. They yield a pseudo-tensor that is not unique.
Usually asserted on the basis of the principle of equivalence that the gravitational energy cannot be localized. (C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation)
OAS Fall 2007 Technical Meeting

4. OAS Fall 2007 Technical Meeting
Linearized GR  GEM Theory
General Relativity (GR)
Gravitoelectromagnetic Theory (GEM)
For “weak” fields
For “weak” fields
See
Bahram Mashhoon, “Gravitoelectromagnetism: A Brief Review,” arXiv:gr-qc/ , 8 Nov 2003
And references therein.
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Negative Sign
Maxwell EM Theory
GEM Theory
Negative Sign
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Maxwell EM Theory Energy Flow
GEM Theory Energy Flow
Negative Sign
Negative Sign
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Energy Flow in GEM Wave − +
A “graviton” carries negative energy in the +k direction
Equivalent to positive energy going in the –k direction
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EM- Radiation from Accelerating Charge
Gravitational Radiation from Accelerating Mass
Negative Sign
Accelerating charge emits radiation that carries positive energy away. Emitting system loses energy.
Accelerating mass emits radiation that carries negative energy away. Emitting system gains energy.
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9. Em′ > Em Stability of Gravitational Bound States DE = - |DE|
Energy r R R’
Em + |DE| M R m Em v
Em → Em′ + DE
Em′ > Em
Em = Em′ + DE
Em′ = Em − DE = Em + |DE|
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Conclusions
Gravitational Radiation carries negative energy away from radiating (accelerating) sources
All gravitational bound states are slowly expanding
Possible physical explanation of Hubble expansion of the Universe
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