CELESTIAL BODIES AND MULTIDIMENSIONAL EINSTEIN THEORY OF GRAVITATION

Static spherically symmetric celestial bodies are investigated in mult idimensional Einstein theory of gravitation. A model with compact Ricc i-nat internal space R(n) is studied and confronted with observations, Integration constants in the exterior solution of held 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 bod y tend to definite limits in the case of large number (n --> infinity) of extra dimensions. As main result it turns out that the model would be in accordance with solar system observational data only if there w ould be a negative (with abnormal targe absolute value) pressure p(1) of solar matter in extra dimensions: \p(1)\ similar to rho c(2), where rho is the matter density.