String Dynamics

A cosmic string has very interesting physical effects. All these effects are originated from its unique way to deform the space-time around it.  A model of an infinitely long, straight cosmic string is one of the exactly solvable systems in General Relativity. Since it is made of vacuum energy rather than ordinary matter, it has a different solution of the Einstein equations, a conic space-time!

Figure 4. Conic space-time formed around a straight string, One complete turn around the string makes up less than by the deficit angle .

The metric around a straight string is given by (in cylindrical coordinates)

where  is the cosmic string parameter (G=Newton constant,  = string energy density). It is a flat space-time metric except for the deficit angle
.
Motion of a cosmic string can be described by Nambu-Goto action,

and it satisfies wave equation. Cosmic strings are expected to have huge tension, tension ~ mass density in natural unit so that their motions are relativistic.
Possible Physical Effects:
(1) Double Images
(2) Kaiser-Stebbins Effect
(3) Wakes
(4) Gravitational Wave Radiation







         

Figure 5. Physical effects by cosmic strings. Kaiser-Stebbins effect, double image, and wake are due to conic space-time around the cosmic string. Radiation of gravitational waves is a generic phenomenon by the time-varying fluctuation of the metric, especially around the cusp.
Kaiser-Stebbins effect is explained in the next page in more detail.

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