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Corrected Article: Wormholes in Einstein-Born-Infeld theory

[Phys. Rev. D 80, 104033 (2009)]
Mart?´n G. Richarte* and Claudio Simeone†
Departamento de F?´sica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria,
Pabello´n I, 1428 Buenos Aires, Argentina
(Received 9 October 2009; published 23 November 2009; corrected initial 15 January 2010; republished 24 May 2010)

"Traversable Lorentzian wormholes [1,2] are topologically nontrivial solutions of the equations of gravity, which would
imply a connection between two regions of the same universe, or of two universes, by a traversable throat. In the case that
such geometries actually exist they could show some interesting peculiarities as, for example, the possibility of using them
for time travel [3,4]. A basic difficulty with wormholes is that the flareout condition [5] to be satisfied at the throat requires
the presence of matter that violates the energy conditions (‘‘exotic matter’’) [1,2,5,6]. It was recently shown [7], however,
that the amount of exotic matter necessary for supporting a wormhole geometry can be made infinitesimally small. Thus, in
subsequent works special attention has been devoted to quantifying the amount of exotic matter [8,9], and this measure of
the exoticity has been pointed as an indicator of the physical viability of a traversable wormhole [10]. Theories beyond the
Einstein-Maxwell framework have been explored with interesting results in this sense [11].

A central aspect of any solution of the equations of gravitation is its mechanical stability. The stability of wormholes has
been thoroughly studied for the case of small perturbations preserving the original symmetry of the configurations. In
particular, Poisson and Visser [12] developed a straightforward approach for analyzing this aspect for thin-shell wormholes,
that is, those which are mathematically constructed by cutting and pasting two manifolds to obtain a new manifold
[13]. In these wormholes the associated supporting matter is located on a shell placed at the joining surface; so the
theoretical tools for treating them is the Darmois-Israel formalism, which leads to the Lanczos equations [14,15]. The
solution of the Lanczos equations gives the dynamical evolution of the wormhole once an equation of state for the matter
on the shell is provided. Such a procedure has been subsequently followed to study the stability of more general spherically
symmetric configurations (see, for example, Ref. [16]), and an analogous analysis has also been carried out in the case of
cylindrical symmetry (see [17]) ...

The generalization of Maxwell electromagnetism to a nonlinear theory in the way proposed by Born and Infeld
introduces a new parameter, which allows for more freedom in the framework of determining the most viable charged
wormhole configurations. If wormholes could actually exist, one would be interested in those that are stable—at least
under the most simple kind of perturbations—and which, besides, require as little amount of exotic matter as possible. Of
course, the case could be that a given change of the theory leads to a worse situation, i.e., that configurations turn out to be
more unstable or require more matter violating the energy conditions as the departure from the standard theory becomes
relevant. However, for large charges, this seems not to be the case with Born-Infeld electrodynamics coupled with
Einstein’s gravity: Here, we have examined the mechanical stability and exotic matter content of thin-shell wormholes
within Einstein-Born-Infeld theory, and as long as large values of the charge are considered, we have found that for small
values of the Born-Infeld parameter, corresponding to a situation far away from the Maxwell limit, the amount of exotic
matter is reduced in relation to the standard case. Thus, if the requirement of exotic matter is considered as the strongest
objection against wormholes, our results suggest that in a physical scenario different from that consistent with present day
observation (as in the early Universe, when nonlinear effects could be more relevant) charged wormholes could have been
more likely to exist."