Gravitational and dilaton radiation from a relativistic membrane

Recent scenarios of the TeV-scale brane cosmology suggest a possibility of existence in the early universe of two-dimensional topological defects: relativistic membranes. Like cosmic strings, oscillating membranes could emit gravitational radiation contributing to a stochastic background of gravitational waves. We calculate dilaton and gravitational radiation from a closed toroidal membrane excited along one homology cycle. The spectral-angular distributions of dilaton and gravitational radiation are obtained in a closed form in terms of Bessel's functions. The angular distributions are affected by oscillating factors due to an interference of radiation from different segments of the membrane. The dilaton radiation power is dominated by a few lower harmonics of the basic frequency, while the spectrum of the gravitational radiation contains also a substantial contribution from higher harmonics. The radiative lifetime of the membrane is determined by its tension and depends weakly on the ratio of two radii of the torus. Qualitatively it is equal to the ratio of the membrane area at the maximal extension to the gravitational radius of the membrane as a whole.