Abstract
AbstractWe extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case wheref(T) gravity becomes the usual linear-in-Tteleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differently when matter fields are present, and thusf(R) gravity andf(T) gravity exhibit different features and cannot be directly re-casted each other.
Highlights
In this work we investigate D-dimensional f (T ) gravity, considering the electromagnetic sector
Enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case where f (T ) gravity becomes the usual linear-in-T teleparallel gravity, that is General Relativity
The dynamical variable of teleparallel gravity is the vierbein field eA(xμ), which forms an orthonormal basis for the tangent space at each point xμ of the manifold, that is eA · eB = ηAB, with ηAB = diag(1, −1, −1, −1)
Summary
Let us investigate the charged solutions of the theory. In order to extract the static solutions we consider the metric form ds. Form (4.7) and (4.8), we deduce that we cannot have simultaneously two non-zero electric field components This result is similar to the known no-go theorem of 3D GR-like gravity [69, 70], which states that configurations with two non-vanishing components of the Maxwell field are dynamically not allowed. It is not valid anymore if we add the magnetic sector, as we will see in subsection 4.3 (it holds only for D=3). In the following we investigate the cases of radial electric field, of non-radial electric field, and of magnetic and radial electric field, separately
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