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 International Conference on Complex Systems (ICCS2007)

Is matter an emergent property of space-time?

Claire Chevalier
ERGA/LERMA Universite Paris 6

Fabrice Debbasch
ERGA/LERMA Universite Paris 6

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     Last modified: September 14, 2007

The first, fully non linear, mean field theory of relativistic
gravitation has been developed in 2004.
The theory makes the striking prediction that averaging or coarse
graining a gravitational field changes the matter content of
space-time. Our contribution presents new calculations that highlight
this effect on black holes of the Reisner-Nordström (RN) family.
Explicit expressions for the equation of state and for the energy and
charge densities of the apparent matter surrounding the coarse grained
black holes are given. In particular, the Schwarzschild black hole,
which is a vacuum solution of Einstein field equations, is shown to
appear after coarse graining as surrounded by an apparent matter whose
equation of state strongly resembles the equation of state commonly
postulated for cosmological dark energy. Taken together, these new
results suggest that matter and charge may be properties of the
space-time which only emerge after a certain coarse graining has been

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