Further matters in space-time geometry:f(R,T,RμνTμν)gravity

摘要: We consider a gravitational theory in which matter is nonminimally coupled to geometry, with the effective Lagrangian of field being given by an arbitrary function Ricci scalar, trace energy-momentum tensor, and contraction tensor tensor. The equations are obtained metric formalism, equation motion massive test particle derived. In this type generally not conserved, nonconservation determines appearance extra force acting on particles field. It interesting note that present theory, explicitly depends entails relevant deviation from geodesic motion, especially for strong fields, thus rendering possibility space-time curvature enhancement ${R}_{\ensuremath{\mu}\ensuremath{\nu}}{T}^{\ensuremath{\mu}\ensuremath{\nu}}$ coupling. Newtonian limit also considered, explicit expression acceleration density small velocity dust particles. analyze detail so-called Dolgov-Kawasaki instability obtain stability conditions respect local perturbations. A particular class can be imposing conservation derive corresponding conservative case using Lagrange multiplier method, action contains independent parameter multiplying divergence cosmological implications investigated both nonconservative cases, several classes exact analytical approximate solutions obtained.