Abstract
In this manuscript, we have presented the compatible solutions under the framework of dynamical and non-dynamical Chern–Simons modified gravity. By taking an open choice of external field as a function of angular parameter $$\theta $$ , we obtained Godel-type solutions of non-dynamical Chern–Simons modified gravity. It is mentioned that a vacuum Godel-type solution exists in this theory. Non-static spherical symmetric solutions are also described for dynamical Chern–Simons modified gravity by considering external field as a function of radial parameter r. Later, results are similar to those of well-known Tolman–Bondi solutions found in the context of general relativity. It is observed that in case of $$\varLambda \rightarrow \kappa p_{0}$$ both parameters A(t, r) and B(t, r) turned to be undefined.
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