Lessons from f(R,R²c,R²m,Lm) gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation, and nonminimal coupling.

This paper studies a generic fourth-order theory of gravity with Lagrangian density f(R, R²C, R²m, Lm), where R²C and R²m respectively denote the square of the Ricci and Riemann tensors. By considering explicit R² dependence and imposing the "coherence condition" fR¹2 = fR² = - fR²/4, the field equations of f(R1.R2.Rl,R2 n,Lm) gravity can be smoothly reduced to that of f(R. G, Lm) generalized Gauss-Bonnet gravity with Q denoting the Gauss-Bonnet invariant. We use Noether's conservation law to study the f(R²mi,R²m...,T²m„,Lm) model with nonminimal coupling between Lm, and Riemannian invariants R1 and conjecture that the gradient of nonminimal gravitational coupling strength ∇fc is the only source for energy-momentum nonconservation. This conjecture is applied to the f(R.R²,R²m,Lm) model, and the equations of continuity and nongeodesic motion of different matter contents are investigated. Finally, the field equation for Lagrangians including the traceless-Ricci square and traceless-Riemann (Weyl) square invariants is derived, t hef(R, R²C, R²m. Lm) model is compared with ihe f(R. R², R²m, T) + 2kLm,„ model, and consequences of nonminimal coupling for black hole and wormhole physics are considered. [ABSTRACT FROM AUTHOR]