Geometry of massless cosmic strings

Abstract

We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the world sheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null rotation or parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string as has been suggested in the past. To illustrate the nonsingular nature of the surrounding geometry, we construct a metric for the massless cosmic string that is smooth everywhere outside the conical singularity.

SU(1,1) solutions for the relativistic quantum particle in cosmic string spacetime

“…At the same time, cosmic strings are also analogous to those found in flux tubes in type-II superconductors [5], [6], [7], [8]. When it comes to the geometry of a single cosmic string, there are various studies done for the geometry generated by them [9], [10], [11] and for the massless ones can be found in [12]. The relativistic quantum dynamics of electric and magnetic dipoles in the presence of a topological defect is studied in [13], fermionic vacuum polarization in the cosmic string spacetime is analyzed in [14].…”

Fundamental frequencies and resonances from eccentric and precessing binary black hole inspirals

“…Comparisons to post-Newtonian predictions for the frequencies of motion would supplement our SF-inspired comparisons to Kerr geodesics. In addition, SF predictions in for Kerr orbits are developing rapidly (e. g. [69,119]), which will allow for a quantitative comparison to analytic approximations, as well as an extraction of higher-order SF effects.…”

“…In this case the ratio of the particle mass µ to that of the Kerr black hole M Kerr serves as a small expansion parameter. While SF results for Kerr are still in development [67][68][69][70], mounting evidence suggests that SF results may be extended much closer to the nearly equal mass cases than expected [71][72][73], which is the regime appropriate for our our high (but not extreme) mass ratio binaries. Meanwhile, the lowest order approximation to the SF-expansion, namely the test particle limit, incorporates the effects of strongly curved spacetime, highly relativistic motion, and is fully understood.…”

Massless cosmic strings in an expanding universe

“…Consider a massless string stretched along the z-axis, which moves along the x-axis at y = 0. A parallel transport of a vector V along a closed contour around the string should result in a non-trivial rotation, V = M (λ)V , where λ = 8πGE and E is an energy of the string per unit length [3]. The string worldsheet is u = y = 0.…”

“…MCS in a flat spacetime can be obtained from common massive cosmic strings [1] as a limiting case, when the velocity of the string reaches the speed of light, mass tends to zero, while energy remains finite [2]. As a result of this limit, a holonomy along a closed countour around a massive string is transformed into a nontrivial holonomy around the MCS [3]. The holonomies of MCS belong to a parabolic subgroup of Lorentz transformations.…”