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

    Hideki Maeda1,* and Cristián Martínez2,3,†

    • *Contact author: h-maeda@hgu.jp
    • †Contact author: cristian.martinez@uss.cl

    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 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 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 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.

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