Effective Einstein theory from metric-affine gravity models via irreducible decompositions

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

“…However, we added in a (1) Q αβ piece. The most general quadratic Lagrangian (D1) is appreciably more complicated than (59). Nevertheless, without our computer algebra programs (see [71], [33], [32]) we would not have been able to handle the messy expressions.…”

“…Let us mention, as examples, the papers [29,34,39,54,59,65,68,76,77,79,82,83,85,86] and references given there. Even possible links to observation were discussed in [1,63,64,66,67,72].…”

“…The most general parity conserving quadratic Lagrangian, which is expressed in terms of the 4 + 3 + 6 + 5 irreducible pieces of Q αβ , T α , W α β , and Z α β , respectively, reads (see [19], [59], [29], and references given):…”

Two-dimensional metric-affine gravity

“…The three 1-forms of torsion and nonmetricity (T, Q, Λ) form the so-called triplet which plays a significant role in the MAG theories in 4 dimensions [11]. As we will see, the triplet of 1-forms is important also for understanding of the 2-dimensional MAG.…”

Nonlinear connections and spinor geometry

“…Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].…”