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A Method of Constructing Off-Diagonal Solutions in Metric-Affine and String Gravity

Sergiu I. Vacaru·Evghenii Gaburov·Denis Gontsa
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Abstract

The anholonomic frame method is generalized for non--Riemannian gravity models defined by string corrections to the general relativity and metric-affine gravity (MAG) theories. Such spacetime configurations are modeled as metric-affine spaces provided with generic off-diagonal metrics (which can not be diagonalized by coordinate transforms) and anholonomic frames with associated nonlinear connection (N-connection) structure. We investigate the field equations of MAG and string gravity with mixed holonomic and anholonomic variables. There are proved the main theorems on irreducible reduction to effective Einstein-Proca equations with respect to anholonomic frames adapted to N-connections. String corrections induced by the antisymmetric H-fields are considered. There are also proved the theorems and criteria stating a new method of constructing exact solutions with generic off-diagonal metric ansatz depending on 3-5 variables and describing various type of locally anisotropic gravitational configurations with torsion, nonmetricity and/or generalized Finsler-affine effective geometry. We analyze solutions, generated in string gravity, when generalized Finsler-affine metrics, torsion and nonmetricity interact with three dimensional solitons.

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Sergiu I. Vacaru, Evghenii Gaburov, Denis Gontsa. 2003-10-16. A Method of Constructing Off-Diagonal Solutions in Metric-Affine and String Gravity. https://arxiv.org/abs/hep-th/0310133

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