  We study torsion properties of the twisted Alexander modules of the affine
complement $M$ of a complex essential hyperplane arrangement, as well as those
of punctured stratified tubular neighborhoods of complex essential hyperplane
arrangements. We investigate divisibility properties between the twisted
Alexander polynomials of the two spaces, compute the (first) twisted Alexander
polynomial of a punctured stratified tubular neighborhood of an essential line
arrangement, and study the possible roots of the twisted Alexander polynomials
of both the complement and the punctured stratified tubular neighborhood of an
essential hyperplane arrangement in higher dimensions. We apply our results to
distinguish non-homeomorphic homotopy equivalent arrangement complements. We
also relate the twisted Alexander polynomials of $M$ with the corresponding
twisted homology jump loci.
