Black Holes, Dark Wormholes and Solitons in f(T) Gravities

Abstract

By choosing an appropriate vielbein basis, we obtain a class of spherically-symmetric solutions in $f(T)$ gravities. The solutions are asymptotic to Minkowski spacetimes with leading falloffs the same as those of the Schwarzschild black hole. In general, these solutions have branch-cut singularities in the middle. For appropriately chosen $f(T)$ functions, extremal black holes can also emerge. Furthermore, we obtain wormhole configurations whose spatial section is analogous to an Ellis wormhole, but $-g_{tt}$ runs from 0 to 1 as the proper radial coordinate runs from $-\infty$ to $+\infty$. Thus a signal sent from $-\infty$ to $+\infty$ through the wormhole will be infinitely red-shifted. We call such a spacetime configuration a dark wormhole. By introducing a bare cosmological constant $Λ_0$, we construct smooth solitons that are asymptotic to local AdS with an effective $Λ_{\rm eff}$. In the middle of bulk, the soliton metric behaves like the AdS of bare $Λ_0$ in global coordinates. We also embed AdS planar and Lifshitz black holes in $f(T)$ gravities. Finally we couple the Maxwell field to the $f(T)$ theories and construct electrically-charged solutions.