Abstract
Static and spherically symmetric wormhole solutions can be reconstructed in the framework of curvature based Extended Theories of Gravity. In particular, extensions of the General Relativity, in metric and curvature formalism give rise to modified gravitational potentials, constituted by the classical Newtonian potential and Yukawa-like corrections, whose parameters can be, in turn, gauged by the observations. Such an approach allows to reconstruct the spacetime out of the wormhole throat considering the asymptotic flatness as a physical property for the related gravitational field. Such an argument can be applied for a large class of curvature theories characterising the wormholes through the parameters of the potentials. According to this procedure, possible wormhole solutions could be observationally constrained. On the other hand, stable and traversable wormholes could be a direct probe for this class of Extended Theories of Gravity.
Highlights
We have developed a strategy to reconstruct WH solutions through Extended Theories of Gravity
In the weak field limit, General Relativity (GR) reduces to the Newtonian theory, but the observations on the rotational curves and on mass-to-light rations of several galaxies showed a clear departure from the classical description
To solve such an issue, modified theories of gravity have been proposed, whose true nature can be reconstructed only by the fit of the data. Such theories solve this observational puzzle by adding to the Newtonian potential a Yukawa-like correction (26), whose parameters can be gauged by the data, see Sect. 3
Summary
Wormholes (WHs) are exotic compact objects characterized by no horizon and singularities, and endowed with a traversable bridge, called WH neck, connecting two universes or two different regions of the same spacetime [1]. Adopting the weak field limit of curvature based Extended Theories of Gravity, where the parameters are gauged by the observations, and comparing them with the WH expansions, one is able to determine the coefficients of the WH metric and reconstruct such solutions within different gravity frameworks with the aim to obtain stable and traversable solutions. This is the central argument on which this paper is based. The article is organized as follows: in Sect. 2 we summarize the properties of static and spherically symmetric WHs; in Sect. 3, the PN expansion in the f (R) gravity framework is discussed as a valid and general paradigm for all curvature based Extended Theories of Gravity; in Sect. 4 we apply the above-mentioned strategy to constrain the WH solutions through the entries of extended gravity models; in Sect. 5 we draw the conclusions
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