2025/06/17 by Maeda, Hideki, Martinez, Cristian
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2506.14872
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.