G?del-type Solutions In F(R) Gravity With An Arbitrary Coupling Between Matter And Geometry

Causality is one of the important issues in the theory of gravity.If closed time-like curves exist in our universe,causality will be broken down.In this paper,by studying the G?del-type solution,we study the issue of causality in the coupling f(R)gravity.The f(R)theory is a modified theory of gravity,which can be obtained by generalizing the Ricci scalar R in the Einstein-Hilbert action of general relativ-ity to be a general function of R.Since this theory can be used to explain the present accelerated cosmic expansion with no need of dark energy,it has spurred an increasing deal of interest.in 1949,G?del obtained the G?del solution,which is one of the famous so-lutions of the Einstein field equation.If the G?del solution permits the existence of closed time-like curves,this solution is a noncausal solution,otherwise it is a causal one.By assuming the perfect fluid and a single massless scalar field as the matter sources respectively,we study the G?del solution in the coupling f(R)theory.We find that the critical radius,beyond which the causality is broken down,is finite in the perfect fluid case,and it is determined by the matter,f(R)model and the coupling parameter.While,for the case of a scalar field as the matter source the critical radius is infinite.Thus,the problem of causalty may exist in the coupling f(R)theory.