Astrophysics and Space Science

, Volume 225, Issue 1, pp 123–135 | Cite as

Celestial bodies and multidimensional Einstein theory of gravitation

  • U. Bleyer
  • L. SH. Grigorian


Static spherically symmetric celestial bodies are investigated in multidimensional Einstein theory of gravitation. A model with compact Ricci-flat internal space ℝ n is studied and confronted with observations. Integration constants in the exterior solution of field equations are determined using integrals over the distribution of matter inside the celestial body. Two independent formulas for the mass and mass squared of the celestial body are derived. The first one is similar to Tolman's formula for the mass in GRT. It is shown that integral parameters (mass, radius etc.) of the matter distribution inside the celestial body tend to definite limits in the case of large number (n → ∞) of extra dimensions.

As main result it turns out that the model would be in accordance with solar system observational data only if there would be a negative (with abnormal large absolute value) pressurep1 of solar matter in extra dimensions: |p1| ∼ρc2, where ρ is the matter density.


Observational Data Solar System Field Equation Matter Density Extra Dimension 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • U. Bleyer
    • 1
  • L. SH. Grigorian
    • 1
  1. 1.WIP-GravitationsprojektUniversität PotsdamPotsdamGermany

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