We consider static spherically symmetric configurations in a Palatini extension of General Relativity including R 2 and Ricci-squared terms, which is known to replace the central singularity by a wormhole in the electrovacuum case. We modify the matter sector of the theory by adding to the usual Maxwell term a nonlinear electromagnetic extension which is known to implement a confinement mechanism in flat space. One feature of the resulting theory is that the non-linear electric field leads to a dynamically generated cosmological constant. We show that with this matter source the solutions of the model are asymptotically de Sitter and possess a wormhole topology. We discuss in some detail the conditions that guarantee the absence of singularities and of traversable wormholes.

The use in the action integral of a volume element of the form Φd D x, where Φ is a metric-independent measure density, can yield new interesting results in all types of known generally coordinate-invariant theories: (1) 4-D theories of gravity plus matter fields; (2) reparametrization invariant theories of extended objects (strings and branes); (3) supergravity theories. In case (1) we obtain interesting insights concerning the cosmological constant problem, inflation and quintessence without the fifth force problem. In case (2) the above formalism leads to dynamically induced tension and to string models of non-abelian confinement. In case (3), we show that the modified-measure supergravity generates an arbitrary dynamically induced cosmological constant, i.e., a new mechanism of dynamical supersymmetry breaking.

We present a review, of recent developments on non-linear gauge theory containing a √ −F 2 term coupled to gravity. We start by showing some of the confining features of this theory in flat space-time. We then consider the coupling, of this non-linear term, to gravity and discuss two types of spherically symmetric solutions. One of them has a tube topology, that is M 2 × S 2 , or of the Levi-Civitta-Robinson-Berttoti (LCRB) type, where the metric coefficient g θθ is a constant. The other type of solutions, Reissner-Nordström-de-Sitter (RNdS), with g θθ = r 2 , where r is a radial variable allowed to have all values from zero to infinity. Next we consider the matching of these solutions via light-like, and subsequently, time-like membranes and show the topologically induced effects of "Hiding of Charge", where a charged particle can appear neutral to an external observer looking at it from the RNdS region, and the "Confining of charge" in a wormhole throat, where two opposite charges are at the opposite sides of a wormhole throats. We proceed with some applications to extended theories of general relativity, in the form of quadratic gravity model (F (R)), then wormholes arise naturally from the non-linear electromagnetic field rather than requiring exotic matter to generate a pre-designed wormhole geometry (Morris-Thorne approach), in another model considered here we have, in addition to quadratic gravity, a dilaton filed (φ), where we find wormhole solutions with de-Sitter asymptotics, and confinement-deconfinement transition effects as function of the dilaton vacuum expectation value. The last application we present is to the "Two Measure theory", where in addition to the metric volume element, √ −g, we consider a new, metric independent, volume element Φ. Finally we conclude and summarize our findings.

The charge-hiding effect by a horned particle, which was studied for the case where gravity/gauge-field system is self-consistently interacting with a charged lightlike brane (LLB) as a matter source, is now studied for the case of a time like brane. From the demand that no surfaces of infinite coordinate time redshift (horizons) appear in the problem we are lead now to a completly explorable horned particle space for traveller that goes through the horned particle (as was the case for the LLB) but now also in addition to this, the horned region is fully visible to a static external observer. This requires negative surface energy density for the shell sitting at the throat. We study a gauge field subsystem which is of a special non-linear form containing a square-root of the Maxwell term and which previously has been shown to produce a QCD-like confining gauge field dynamics in flat space-time. The condition of finite energy of the system or asymptotic flatness on one side of the horned particle implies that the charged object sitting at the throat expels all the flux it produces into the other side of the horned particle, which turns out to be of a "tube-like" nature. An outside observer in the asymptotically flat universe detects, therefore, apparently neutral object. The hiding of the electric flux behind the tube-like region of a horned particle is the only possible way that a truly charged particle can still be of finite energy, in a theory that in flat space describes confinement. This points to the physical relevance of such solutions, even though there is the need of *

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