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

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.Comment: 32 pages, 1 figure, PTPTeX ver.0.8 (LateX2e), Accepted for publication to Progress of Theoretical Physic

Does a Nambu-Goto wall emit gravitational waves? -- Cylindrical Nambu-Goto wall as an example of gravitating non-spherical walls --

Gravitational field of a cylindrical Nambu-Goto wall in the vacuum spacetime is considered in order to clarify the interaction between Nambu-Goto membranes and gravitational waves. If one neglects the emission of gravitational waves by the wall motion, the spacetime becomes singular. It is also shown that the emission of gravitational waves does occur by the motion of the cylindrical wall if the initial data is singularity free. The energy loss rate due to radiation of gravitational waves agrees with that estimated from the test wall motion and the quadrupole formula for the gravitational wave emission. This is quite different from the oscillatory behavior of gravitating Nambu-Goto membranes: the presence of gravity induces the wall to lose its dynamical degree of freedom.Comment: Accepted for publication in Physical Review D. Minor changes are made, and some typos are correcte

Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status

The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar field. Through this review, we point out the problems which should be clarified for the further theoretical sophistication of this perturbation theory. We also expect that this theoretical sophistication will be also useful to discuss the theoretical predictions of Non-Gaussianity in CMB and comparison with observations.Comment: 26 pages, 2 figures, Summary report on the current status of the second-order gauge-invariant cosmological perturbation theory, Published as an invited review in the Special Issue "Testing the Gaussianity and Statistical Isotropy of the Universe" in Advances in Astronom