Celestial bodies and multidimensional Einstein theory of gravitation
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.
KeywordsObservational Data Solar System Field Equation Matter Density Extra Dimension
Unable to display preview. Download preview PDF.
- Avakian, R.M.: 1990,Astrofizika 33, 429.Google Scholar
- Avakian, R. M., Bleyer, U., Chubarian, E. V. and Grigorin, L. Sh.: 1994, New mass formula for spherically symmetric stellar configurations, AIP preprint (Potsdam) 94-9.Google Scholar
- Bleyer, U., Bronnikov, K.A., Mclnikov, V.N. and Fadeev, S.B.: 1994, On black hole stability in multidimensional gravity, AIP preprint (Potsdam) 94-01.Google Scholar
- Grigorian, L.Sh. and Sahakian, G.S.: 1983,Astrophys. Space Sci. 95, 305.Google Scholar
- Grigorian, L.Sh., Saharian, A.A.: 1990,Astrophys. Space Sci. 167, 271.Google Scholar
- Hellings, R.: 1983,Phys. Rev. Lett. 51, 1609.Google Scholar
- Ivashchuk, V. D. and Melnikov, V. N.: 1994,Class. and Quant. Grav., (submitted).Google Scholar
- Landau, L. D. and Lifshiz, E.M.: 1971,The Classical Theory of Fields, Addison-Wesley.Google Scholar
- Melnikov, V.N.: 1993, Centro Brasileiro de Pesquisas Fisicas, to appear in the proceedings of the 1993 summer school.Google Scholar
- Misner, C.W., Thorne, K.S. and Wheeler, J.A.: 1973,Gravitation, W.H. Freeman, San Francisco.Google Scholar
- Myers, R. C. and Perry, M. J.: 1986,Ann. of Phys. 172, 304.Google Scholar
- Myers, R.C.: 1987,Phys. Rev. D 35, 455.Google Scholar
- Saakian, G.S.: 1974,Equilibrium Configurations of Degenerate Gaseous Masses, Halsted (Wiley), New York.Google Scholar
- Schmutzer, E.: 1988,Ann. Phys. (Leipzig),45, 578.Google Scholar
- Schwarzschild, M.: 1958,Structure and Evolution of the Stars, Princeton University Press, Princeton.Google Scholar
- Tangherlini, F. R.: 1963,Nuovo Cim. 27, 636.Google Scholar
- Will, C. M.: 1981,Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge.Google Scholar
- Yoshimura, M.: 1986,Phys. Rev. D 34, 1021.Google Scholar