Exact plane symmetric black bounce with a perfect-fluid exterior obeying a linear equation of state
Phys. Rev. D 112, 044021 – Published 13 August, 2025
DOI: https://doi.org/10.1103/lt5f-gqmw
Abstract
We investigate an exact two-parameter family of plane symmetric solutions admitting a hypersurface-orthogonal Killing vector in general relativity with a perfect fluid obeying a linear equation of state in dimensions obtained by Gamboa in 2012. The Gamboa solution is identical to the topological Schwarzschild–Tangherlini–(anti–)de Sitter -vacuum solution for and admits a nondegenerate Killing horizon only for and . We identify all possible regular attachments of two Gamboa solutions for at the Killing horizon without a lightlike thin shell, where may have different values on each side of the horizon. We also present the maximal extension of the static and asymptotically topological Schwarzschild-Tangherlini Gamboa solution, realized only for , under the assumption that the value of is unchanged in the extended dynamical region beyond the horizon. The maximally extended spacetime describes either (i) a globally regular black bounce whose Killing horizon coincides with a bounce null hypersurface or (ii) a black hole with a spacelike curvature singularity inside the horizon. The matter field inside the horizon is not a perfect fluid but rather an anisotropic fluid that can be interpreted as a spacelike (tachyonic) perfect fluid. A fine-tuning of the parameters is unnecessary for the black bounce, but the null energy condition is violated everywhere except on the horizon. In the black-bounce (black-hole) case, the metric in the regular coordinate system is only for with odd (even) satisfying , and if one of the parameters in the extended region is fine-tuned.