Does a physical field have to share the symmetries of the ambient spacetime?
Open a typical textbook on classical electrodynamics and you will find numerous examples of wrinkled and twisted electromagnetic fields, in a sheer contrast with the maximally symmetric Minkowski spacetime they inhabit. These, however, are the weak fields which do not “bend” the spacetime “fabric”. Once we allow the field to interact with the spacetime geometry via gravitational field equations, the symmetry constraints become much more stringent. When the answer to the opening question is affirmative we say that the field inherits the spacetime symmetries. Symmetry inheritance is not only used as a convenient assumption in a choice of the ansatz, but is also an important ingredient of Continue reading