Abstract
We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.
Highlights
We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist
We find a center in the geometry defined by hμν and a two-sphere of area A = 4πrc2 in the physical geometry
Note that in GR the geometry extends down to z = 0, whereas for λ > 0 we find that z cannot be smaller than zc, which manifests the existence of a finite structure replacing the central point-like singularity
Summary
We assume vanishing torsion, i.e., Γλ[μν] = 0, though impose this condition a posteriori, once the field equations have been obtained (see [24] for details). This implies that the Ricci tensor is symmetric, i.e., R[μν] = 0. We see that the term in brackets only depends on the metric gμν and T, which implies that the connection Γλμν appears linearly in this equation and can be solved by algebraic means. As in previous works [20, 25], here we shall take the strategy of solving the field equations in terms of hμν and use Σin (2.11) to obtain the physical metric gμν
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