Generating Black Strings in Higher Dimensions

Abstract

Starting with a Zipoy-Voorhees line element we construct and study the three parameter family of solutions describing a deformed black string with arbitrary tension.

Time-dependent hypercylindrical spacetimes

“…The metric is asymptotically flat, as previously was observed in (9), for this reason, the boundaries of the Penrose diagram are the same as in a Minkowsky diagram.…”

“…In [9] this case corresponds to the spherical symmetry, in the present context it corresponds to the time-dependent analog of the Kim and Lee [11] black string with arbitrary tension. In what follows we shall study the asymptotic behavior of the time-dependent solution (4).…”

“…In [9] a 5D generalized black string solution was obtained by dressing with a scalar field the Zipoy-Voorhees solution and then lifted to the fifth dimension. In this section this solution is transformed via a Wick rotation into a time-dependent cylindrical spacetime.…”

“…See [9] for details. Using a double analytic continuation or Wick rotation, t → i z and z → it, the metric (1) becomes a 5D time-dependent cylindrically symmetric one given by,…”

“…2 we transform the 5D black string [9] via a Wick rotation, to the form of the generalized Einstein-Rosen space-time, having a local behavior of gravitational waves, next in Sect. 3 the asymptotic behavior of the solution is studied then in Sect.…”