Palatini Nonlinear Electrodynamics

The general subject of this talk is the formalism for electromagnetism and its non-linear generalizations, which is analogous to the Palatini formalism of General Relativity and its extensions and modifications. There exist already studies of non-linear electrodynamics (NLED) in first order formalism of a limited type where it is always equivalent to the second order formalism. The advantage of this first order approach is mainly technical in that it facilitates the study of certain NLED theories which are difficult to handle in second order.

However, it turns out that it is possible to construct a large family of first order NLED theories which we call Palatini non-linear electrodynamics (PNLED for short), by relinquishing the condition of equivalence between the first and second order formalism.

In this talk I will present some of the implications (mainly gravitational) of PNLED in two complementary domains: on one hand small scale objects like black holes and soliton-like objects, and on the other hand, application to cosmology.