Unconventional string-like singularities in flat spacetime

Abstract

The conical singularity in flat spacetime is mostly known as a model of the cosmic string or the wedge disclination in solids. Its another, equally important, function is to be a representative of quasiregular singularities. From all these of views it seems interesting to find out whether there exist other similar singularities. To specify what "similar" means I introduce the notion of the string-like singularity, which is, roughly speaking, an absolutely mild singularity concentrated on a curve or on a 2-surface S (depending on whether the space is three- of four-dimensional). A few such singularities are already known: the aforementioned conical singularity, two its Lorentzian versions, the "spinning string", the "screw dislocation", and Tod's spacetime. In all these spacetimes S is a straight line (or a plane) and one may wonder if this is an inherent property of the string-like singularities. The aim of this paper is to construct string-like singularities with less trivial S. These include flat spacetimes in which S is a spiral, or even a loop. If such singularities exist in nature (in particular, as an approximation to gravitational field of strings) their cosmological and astrophysical manifestations must differ drastically from those of the conventional cosmic strings. Likewise, being realized as topological defects in crystals such loops and spirals will probably also have rather unusual properties.

Draft. References and comments are welcome. v2. Section 3 is intact, the rest is made briefer and clearer. A couple of references are added. v3. Insignificant correstions. The published version

References in corpus (7)

• Cosmic strings
• Volterra Distortions, Spinning Strings, and Cosmic Defects
• The use of Generalised Functions and Distributions in General Relativity
• Simple Quantum Systems in Spacetimes with Closed Timelike Curves
• The quantum inequalities do not forbid spacetime shortcuts
• The time travel paradox
• Kinks and Time Machines

Cited by in corpus (8)

• Space-Times with Integrable Singularity
• The Geometry of Massless Cosmic Strings
• Even the Minkowski space is holed
• Semiclassical backreaction around a nearly spinning cosmic string
• Unwrapping Closed Timelike Curves
• Gravitational strings. Do we see one?
• Singularity at the demise of a black hole
• Quasiregular singularities taken seriously