Jps. Lemos et Vt. Zanchin, 3-DIMENSIONAL BTZ BLACK-HOLE AS A CYLINDRICAL SYSTEM IN 4-DIMENSIONALGENERAL-RELATIVITY, Physical review. D. Particles and fields, 53(8), 1996, pp. 4684-4686
It is shown how to transform the three-dimensional BTZ black hole into
a four-dimensional cylindrical black hole (i.e., black string) in gen
eral relativity. This process is identical to the transformation of a
point particle in three dimensions into a straight cosmic string in fo
ur dimensions.