Description
I will talk about static spacetimes that are spherically symmetric in three space dimensions, and have also n extra dimensions with Euclidean symmetry. I show that a specific ansatz leads to a limited set of vacuum solutions of the Einstein field equations, which can also be classified as Weyl solutions. I will talk about properties of these spacetimes investigated through the Kretschmann scalar, Newtonian mass defined through the Newtonian limit, Komar mass, Einstein, Landau--Lifshitz, and ADM mass. In addition to 1+3+n dimensional Minkowski spacetime, there are two classes of solutions. The first class is a trivial product of the Schwarzschild spacetime and Euclidean spaces in extra dimensions, while the second class is non-trivial. In the case with no horizon, there is a naked singularity, all masses are equal, and they are negative. In the case when there is a horizon, this horizon accommodates a physical singularity, which corresponds to Kaluza--Klein bubbles featuring exotic properties. Einstein, Landau--Lifshitz, and ADM masses are positive, while Newtonian and Komar masses are negative. This differentiates these solutions from trivial higher-dimensional extensions of the Schwarzschild solution.