The form of cosmic string cusps

We classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts. A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp. The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation. We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation. We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core. The result is that the energy scales as √ rL instead of the usual value of r1/3L2/3, where r is the string radius and L and is the typical length scale of the string. Since r L for cosmological strings, the radiation is strongly suppressed and could not be observed. 98.80.Cq Typeset using REVTEX ∗Email address: [email protected] †Email address: [email protected]