Field Energy in GEM Field Theory

1
Field Energy in GEM Field Theory

• W. J. Wilson
• Department of Engineering and Physics
• University of Central Oklahoma
• Edmond, OK 73034

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Outline

1. The Field Energy Problem of GR
2. Linearized GR ? GEM Theory
3. Analogy of GEM with Maxwell EM Theory
4. Gravitational Field Energy in GEM Theory
5. Gravitational Radiation in GEM Theory
6. Stability of Gravitational Bound States in GEM
7. Conclusions

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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)

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Linearized GR ? GEM Theory
General Relativity (GR)
Gravitoelectromagnetic Theory (GEM)
For weak fields
For weak fields
See Bahram Mashhoon, Gravitoelectromagnetism A
Brief Review, arXivgr-qc/0311030, 8 Nov 2003
And references therein.
OAS Fall 2007 Technical Meeting
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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
Accelerating mass emits radiation that carries
negative energy away. Emitting system gains
energy.
Accelerating charge emits radiation that carries
positive energy away. Emitting system loses
energy.
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8/10
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Stability of Gravitational Bound States
DE - DE
Energy
r
R
R
Em DE
M
R
Em
m
v
Em ? Em' DE
Em' gt 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

OAS Fall 2007 Technical Meeting
10/10