Some Cosmological Consequences of Negative Gravitational Field Energy

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Some Cosmological Consequences of Negative
Gravitational Field Energy

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

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Outline

1. The Field Energy Problem of for Gravitation
2. Analogy of GEM with Maxwell EM Theory
3. Gravitational Field Energy in GEM Theory
4. Spherical Solution Event Horizon
5. Friedman Cosmology Model with Gravitational Field
   Energy
6. Summary/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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The Field Energy Problem of GR

• Both standard Newtonian Gravitation and the
  Maxwell-form Gravitomagnetic (GEM) theory of
  Gravity have a gravitational field energy
  (density)
• This gravitational field energy has been
  discounted because it is negative.
• By the E M c2 mass equivalence relation this
  gravitational field energy density is equivalent
  to the negative mass density

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Negative Sign
Maxwell EM Theory
GEM Theory
Negative Sign
OAS Fall 2008 Technical Meeting
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Maxwell EM Theory Energy Flow
GEM Theory Energy Flow
Negative Sign
Negative Sign
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Static GEM Theory
Reduces to Newtonian Gravitation (with extra
nonlinear term
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7/13
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Spherically Symmetry
For empty space ? 0, so
Look for Spherical symmetric solution
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Spherically Symmetry (cont)
This has the general solution
Where B is an integration constant. Using the
boundary condition,
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9/13
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Event Horizon
This solution
Can be written as
where
Is the usual Schwarzschild Radius
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10/13
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Negative Energy in Cosmological Model
This field
For a mass m at the edge of the universe at R(t)
satisfies the equation of motion
Which has the first integral
Friedman-like equation for expanding universe
cosmology in this model
OAS Fall 2008 Technical Meeting
11/13
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Negative Energy in Cosmological Model
Produces expanding Universe model with positive
radial acceleration
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Summary

• Gravitational Field Energy give mechanism
  explanation of Hubble expansion of the Universe
  with acceleration Dark Energy
  Gravitational Field Energy ??
• Can gravitational collapse produce effective
  negative mass black holes?

OAS Fall 2008 Technical Meeting
13/13