Four-dimensional regular black strings in bilocal gravity

In this paper, we obtain a static black string solution for a bilocal gravitational source in 3+1 dimensions. The solution is regular at the origin and tends asymptotically to the ordinary static uncharged black string solution of general relativity. It allows an event horizon and an internal horizon depending on the value of the mass density. A mass remnant associated with a vanishing Hawking temperature is also found. In order to stabilize the solution, a perfect cosmological fluid with state parameter omega > -1 should be present throughout space. However, energy conditions do not exclude an exotic substance nearby the black string. Finally, we find the stationary counterpart of the solution and analyze the behavior of the horizons according to the mass and angular momentum of the spinning object.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, the authors obtain a static black string solution for a bilocal gravitational source in 3+1 dimensions. The solution is regular at the origin and approaches the ordinary static uncharged black string solution of general relativity asympotically. It allows the existence of an event horizon and an internal horizon depending on the mass density. The authors also find a mass remnant associated with a vanishing Hawking temperature. To stabilize the solution, a perfect cosmological fluid with state parameter omega > -1 needs to be present throughout space. However, the energy conditions do not rule out the presence of exotic matter near the black string. Additionally, the authors find the stationary counterpart of the solution and analyze the behavior of the horizons based on the mass and angular momentum of the spinning object.