Electromagnetic and gravitational Hopfions

Hopfions are a family of `solitonary’ field solutions which have non-trivial topological structure. I will focus on two physical applications of Hopfions: electromagnetism and linear gravitation. I will show that electromagnetic ( or linearized gravity) field can be quasi-locally described in terms of complex scalar field. New definition of topological charge for linearized gravity will be presented. Using Hopfion solution, I will discuss problem of energy in linearized gravitation.