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We investigate geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and characterized by tension and mass densities. The solutions are classified by the tension-to-mass ratio. One particular example is the well-known Schwarzschild black string which has a curvature singularity enclosed by a horizon. We focus mainly on geometry of other solutions which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer with finite time, but is infinitely red-shifted.
We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the ratio of stri
We study the free massive scalar field in de Sitter spacetime with static charts. In particular, we find positive-frequency modes for the Bunch-Davies vacuum state natural to the static charts as superpositions of the well-known positive-frequency mo
In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the $O(4)$ Fock vacuum of Allen and Folacci nor from the non-Fo
We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay ra
This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of t