N-index D dimensional Einstein gravitatational field equations completely geometrized

Aim:

The possibility of the geometrization of the 2-index, 4-index and the n-th index Einstein field equations under conditions of D space-time dimensions has been investigated.

Methods:

The usual tensor calculus rules were used. New rules of tensor calculus were developed too.

Results:

The 2-index, 4-index and the n-th index stress-energy-tensor (8×π×γc⁴)×T_μν has been geometrized under conditions of D dimensions. The Ricci tensor R_μν has been expressed completely in terms of the metric tensor g_μν under conditions of D dimensions too. Based on the geometrized Einstein field equations under conditions of D dimensions, a procedure how to calculate the  value of the cosmological constant Λ depending on the D space-time dimensions has been developed.

Conclusion:

The n-index Einstein field equations under conditions of D dimensions open the door to a logically consistent unified field theory