A snapping cosmic string in a de Sitter or anti-de Sitter universe

Abstract

We present and describe an exact solution of Einstein's equations which represents a snapping cosmic string in a vacuum background with a cosmological constant Λ. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of Λ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson-Trautman waves. It is also derived as a limit of the C-metric with Λ, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.

Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

“…In the latter case, a nonvanishing cosmological constant can also be considered. This leads to a specific expanding spherical impulse generated by a snapping cosmic string in the (anti-)de Sitter universe [17].…”

The global uniqueness and C 1 -regularity of geodesics in expanding impulsive gravitational waves

“…The family of such sandwich waves was introduced by Griffiths and Docherty in [44] and further studied in [13] for all possible values of Λ and signs of . The metric has the Robinson-Trautman canonical form (13), (14), with the function F (ζ, u) taken to be…”

“…This line element is related to (13) via the transformation ξ ≡ F (ζ, u) with F ,u = f (F (ζ, u), u), see [11,47]. With the specific choice (15) convenient for sandwich and impulsive waves, this corresponds to [14] f (ξ, u) = (g /g) ξ log ξ .…”

“…see [14]. However, observe that the form of the metric (20) with (22) has to be considered as being only formal, since it is quadratic in f and so explicitly contains a square of the Dirac δ.…”

Topological mass term in effective Brane-World scenario with torsion

“…One finds objects analogous to these topological defects in condensed matter systems (where there is no gravity) for example in flux tubes in type-II superconductors [16], or vortex filaments in a superfluid [17]. Interesting discussions of cosmic strings in brane world scenario can be found in refs [18,19,20] It is important to remark that KR fields have already been introduced in the cosmic string context with dilaton gravity [21,22] and in global vortex with extra dimensions [23]. They are an important ingredient to described vortex configuration in condensed matter systems [24,25,16,17].…”