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Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity | | Ednaldo L. B. Junior
; Manuel E. Rodrigues
; Mahouton J. S. Houndjo
; | | Date: |
24 Mar 2015 | | Abstract: | We investigate $f(T)$ theory coupled with a nonlinear source of
electrodynamics, for a spherically symmetric and static spacetime in $4D$. We
re-obtain the Born-Infeld and Reissner-Nordstrom-AdS solutions. We generalize
the no-go theorem for any content that obeys the relationship
$mathcal{T}^{;;0}_{0}=mathcal{T}^{;;1}_{1}$ for the energy-momentum
tensor and a given set of tetrads. Our results show new classes of solutions
where the metrics are related through $b(r)=-Na(r)$. We do the introductory
analysis showing that solutions are that of asymptotically flat black holes,
with a singularity at the origin of the radial coordinate, covered by a single
event horizon. We also reconstruct the action for this class of solutions and
obtain the functional form $f(T) = f_0left(-T
ight)^{(N+3)/[2(N+1)]}$ and
$mathcal{L}_{NED} = mathcal{L}_0left(-F
ight)^{(N+3)/[2(N+1)]}$. Using the
Lagrangian density of Born-Infeld, we obtain a new class of charged black holes
where the action reads $f(T) = -16eta_{BI} left[1 - sqrt{1 +
(T/4eta_{BI})}
ight]$. | | Source: | arXiv, 1503.7427 | | Services: | Forum | Review | PDF | Favorites | |
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