(1+4)-dimensional spherically symmetric black holes in f(T)

Abstract

New non-vacuum spherically symmetric solutions in (1+4)-dimensional space-time are derived using the field equations of f(T) theory, where T is the torsion scalar defined as \(T\mathop = \limits^{def} {T^\mu }_{\nu \rho }S_\mu ^{\nu \rho }\). The energy density, radial and transversal pressures in these solutions are shown to satisfy the energy conditions. Other interesting solutions are obtained under the constraint of vanishing radial pressure for different choices of f(T). Impositions are provided to reproduce the (1+4)-dimensional AdS-Schwarzschild solution. In the quadratic case, i.e., f(T) ∝ T², other impositions are derived and have shown to satisfy the non-diagonal components of the field equations of f(T) theory. The physics relevant to the resulting models is discussed.