Born-Infeld inspired modifications of gravity

General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.Comment: 212 pages, Review under press at Physics Report

Can Non Gravitational Black Holes Exists?

We claim that the existence of a mechanism such that photons may be trapped in a compact domain is not an exclusive property of gravitational forces. We show the case in which a non-linear electrodynamics allows such effect. In this latter case we should call this region an Electromagnetic Black Hole (EBH).Comment: 11 pages, LaTex, no figures, revised versio

Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics

We show that there is a function of one variable's worth of Lagrangians for a single Maxwell field coupled to gravity whose equations of motion admit electric-magnetic duality. Such Lagrangians are given by solutions of the Hamilton-Jacobi equation for timelike geodesics in Witten's two-dimensional black hole. Among them are the Born-Infeld Lagrangian which arises in open string theory. We investigate the effect of the axion and the dilaton in the open superstring case and we show that this theory loses its electric-magnetic duality invariance when one considers the higher order electromagnetic field terms. We discuss some implications for black holes in string theory and an extension to $2k$-forms in $4k$ spacetime dimensions.Comment: 27 pages Latex. Revised version including new section on open string theory in which we find the inclusion of the axion breaks the electric-magnetic duality symmetry when one considers higher order electomagnetic field terms. To appear in Nucl Phys

Non-linear effects on radiation propagation around a charged compact object

The propagation of non-linear electromagnetic waves is carefully analyzed on a curved spacetime created by static spherically symmetric mass and charge distribution. We compute how non-linear electrodynamics affects the geodesic deviation and the redshift of photons propagating near this massive charged object. In the first order approximation, the effects of electromagnetic self-interaction can be distinguished from the usual Reissner-Nordstr\"om terms. In the particular case of Euler-Heisenberg effective Lagrangian, we find that these self-interaction effects might be important near extremal compact charged objects.Comment: 7 pages, no figures, new references added, minor corrections in some equation

Penrose limits, supergravity and brane dynamics

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born--Infeld type.Comment: 67 page