Abstract
This paper studies a generic fourth-order theory of gravity with Lagrangian density , where and respectively denote the square of the Ricci and Riemann tensors. By considering explicit dependence and imposing the “coherence condition” , the field equations of gravity can be smoothly reduced to that of generalized Gauss-Bonnet gravity with denoting the Gauss-Bonnet invariant. We use Noether’s conservation law to study the model with nonminimal coupling between and Riemannian invariants , and conjecture that the gradient of nonminimal gravitational coupling strength is the only source for energy-momentum nonconservation. This conjecture is applied to the 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, the model is compared with the model, and consequences of nonminimal coupling for black hole and wormhole physics are considered.
- Received 15 May 2014
DOI:https://doi.org/10.1103/PhysRevD.90.024059
© 2014 American Physical Society