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

TL;DR

This paper compares the oscillatory behaviors of gravitating and test Nambu-Goto strings using gauge-invariant perturbation techniques, revealing that gravitational waves fully determine the string's dynamical degrees of freedom without contradicting test string dynamics.

Contribution

It demonstrates that the dynamical behavior of an infinite gravitating Nambu-Goto string is governed by gravitational waves, aligning with previous findings and clarifying the relationship with test string dynamics.

Findings

Dynamical degrees of freedom are determined by gravitational waves.

No contradiction between gravitating and test string behaviors.

Existence of an exact pp-wave solution supports the analysis.

Abstract

Comparison of the oscillatory behavior of a gravitating infinite Nambu-Goto string and a test string is investigated using the general relativistic gauge invariant perturbation technique with two infinitesimal parameters on a flat spacetime background. Due to the existence of the pp-wave exact solution, we see that the conclusion that the dynamical degree of freedom of an infinite Nambu-Goto string is completely determined by that of gravitational waves, which was reached in our previous works [K. Nakamura, A. Ishibashi and H. Ishihara, Phys. Rev. D{\bf 62} (2002), 101502(R); K. Nakamura and H. Ishihara, Phys. Rev. D{\bf 63} (2001), 127501.], do not contradict to the dynamics of a test string. We also briefly discuss the implication of this result.