Exact plane symmetric black bounce with a perfect-fluid exterior obeying a linear equation of state

Abstract

We investigate an exact two-parameter family of plane symmetric solutions admitting a hypersurfaceorthogonal Killing vector in general relativity with a perfect fluid obeying a linear equation of state p = χρ in n(≥ 4) dimensions obtained by Gamboa in 2012. The Gamboa solution is identical to the topological Schwarzschild–Tangherlini–(anti–)de Sitter Λ-vacuum solution for χ = −1 and admits a nondegenerate Killing horizon only for χ= −1 and χ ∈ [−1/3,0). We identify all possible regular attachments of two Gamboa solutions for χ ∈[−1/3,0) at the Killing horizon without a lightlike thin shell, where χ 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 χ ∈ (−(n − 3)/(3n − 5),0), under the assumption that the value of χ 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 finetuning 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 C∞ only for χ = −1/(1 + 2N) with odd (even) N satisfying N?> (n − 1)/(n − 3), and if one of the parameters in the extended region is fine-tuned.