ABSTRACTThe general theory of relativity is currently established as the most precise theory of gravity supported by observations, and its application is diverse ranging from astronomy to cosmology, while its application to astrophysics has been restricted only to compact stars due to the assumption that the Newtonian approximation is sufficient for celestial bodies with medium density such as the sun. Surprisingly, the recent research of the author has implied that this long‐held assumption is not valid, and that nonperturbative effects significantly change relevant results obtained by Newtonian gravity. In particular, local physical quantities inside the sun are newly predicted to exhibit power law differently from the so‐called standard solar model. This surprising result is reviewed including brief discussion of physics behind the discrepancy and a little new application.