Gravitational and electromagnetic field of static and ultrarelativistic objects in nonlocal theory

Abstract

This thesis studies solutions of nonlocal modifications of Maxwell and linearized gravity equations. We focus on a wide class of Lorentz invariant theories known as ghost free models in which a form factor of nonlocality is chosen so that no new additional unphysical degrees of freedom are present. Such form factors introduce a length scale $\ell$ that determines the range in which the effects of nonlocality are important. Using the Green function method we obtain solutions in such theories for stationary fields created by point-like and extended objects. By performing the boost transformations of the obtained stationary solutions and taking the Penrose limit we obtain solutions of the nonlocal theory describing the electromagnetic and gravitational field of ultrarelativistic objects. The key role in this derivation is played by a property of the factorization of the Green functions in the Penrose limit. The properties of electromagnetic and gravitational fields of ultrarelativistic objects are discussed and concrete examples are presented.