Kerr geometry in $$f(T)$$ f ( T ) gravity

Abstract

Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f (T ) theories of gravity.

Regular black holes inf(T) Gravity through a nonlinear electrodynamics source

“…Through the above expressions and the ones of Euler-Lagrange 11) and by multiplying all by the factor e −1 e a β /4, we get the following equations of motion 2.12) where T µ β is the energy-momentum tensor of non-linear electrodynamics source…”

“…in [10] with spherical symmetry, and [11] with axial symmetry. The solution of Reissner-NordstromAdS (and their particular cases) was re-obtained in [12], and also with new charged solutions in f (T ) Gravity, where f (T ) was reconstructed by a parametric method.…”

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

“…(T ) quantitatively. Taking suitable values for the constants in (25) to match the early time of the empty universe. So we take an initial scale factor a 0 = 4.3 × 10 −13 , Hubble constant H 0 = 10 10 s −1 , initial time at Planck time t 0 = t p = 10 −44 s. Also, as f (T ) ∼ Λ at the limit t ∼ t f , we take the constant Λ = 10 −30 s −2 to match the measured value of the cosmological constant by the cosmological and astrophysical observations.…”

“…Equation (25) indicates that f (T ) has a decaying behaviour, so that f (T ) :∼ 2.76 × 10 87 s −2 → 10 −30 s −2 as t : t p → t f . The plots of Figure 2(b) show that the time interval of this decay is at t f ∼ 10 −12 − 10 −10 s; then it fixes its value to the present value of the cosmological constant.…”

“…The f (T ) theories have paid more attention in the last decade to exploring different aspects in astrophysics [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and in cosmology [28][29][30][31][32][33][34][35][36][37][38]. Some applications show interesting results, e.g.…”