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f(T) gravity, a generally modified teleparallel gravity, has become verypopular in recent times as it is able to reproduce the unification of inflationand late-time acceleration without the need of a dark energy component or aninflation field. In this present work, we investigate specifically the range ofvalidity of Birkhoff's theorem with the general tetrad field via perturbativeapproach. At zero order, Birkhoff's theorem is valid and the solution is thewell known Schwarzschild-(A)dS metric. Then considering the special case of thediagonal tetrad field, we present a new spherically symmetric solution in theframe of f(T) gravity up to the perturbative order. The results with thediagonal tetrad field satisfy the physical equivalence between the Jordan andthe so-called Einstein frames, which are realized via conformal transformation,at least up to the first perturbative order.

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order