We discuss static, spherically symmetric solutions to the 5D Einstein- Maxwell equations (belonging to wide classes of multidimensional solutions known at least from the 1990s) and select among them those which must observationally look like local objects whose surface reflects back particles or signals getting there, the so-called mirror stars (also called “topological stars” by some authors). Their significant parameters are the Schwarzschild mass m and the magnetic charge q, such that q2 > 3m2 , while the radius of their mirror surface is rb = 2q2 /(3m) > 2m. We also discuss their black hole counterparts for which q2 ≤ 3m2 . For both these objects, we study spherically symmetric time-dependent perturbations and determine the stability regions in their parameter spaces. Thus, mirror stars turn out to be stable only at rb < rb ≈ 4.004m, while the black holes prove to be stable in the whole range of their parameters. We calculate the fundamental frequencies and decay rates of black hole perturbations using the WKB and time domain methods. Our stability results disagree with some of those previously announced in the literature.
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