Black strings from dark matter

Abstract

In this paper, we obtain two static black string solutions by considering as sources axisymmetric dark matter (DM) distributions in 3+1 dimensions, in two different scenarios, namely, purely isotropic and radial orbits, which are regulated by two DM parameters. Both solutions tend asymptotically to the usual static and uncharged black string vacuum solution predicted by General Relativity (GR), and each of them presents an event horizon, which is larger than the one corresponding to the vacuum solution, as it is shown. We also show that the presence of DM turns these solutions singular at their symmetry axis. Then, we calculate the Hawking temperatures of these black string horizons and discuss some of their consequences. Unlike what occurs with the static black string vacuum solution, we find that there exists a linear density of mass (or tension) remnant associated with a vanishing Hawking temperature for the solutions under consideration. Thus, we analyze how the presence of DM affects the occurrence of the remnants. Further, we calculate other thermodynamic quantities, namely entropy, heat capacity, and free energy per unit length, showing that thermal phase transitions can occur in the presence of DM. We also analyze the weak (and null) energy conditions and conclude that DM does not behave like an exotic fluid. Finally, the corresponding stationary solutions are obtained, as well as their new tensions as functions of both the mass and angular momentum of the black strings.