Comparison of the oscillatory behaviors of a gravitating Nambu-Goto string with a test string

Comparison of oscillatory behaviors of a gravitating infinite Nambu-Goto string with a test string is discussed using the general relativistic gauge invariant perturbation technique with two infinitesimal parameters on the flat spacetime background. Due to the existence of the pp-wave exact solution, we see that the conclusion “dynamical degree of freedom of an infinite Nambu-Goto string is completely determined by that of gravitational waves”, which is obtained in our previous works, 2) is not contradict to the dynamics of a test string. We also discuss the implication of this result, briefly.