Null vectors of the WBC2WBC_2 algebra

Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones described by Benoit and Saint-Aubin and analogues of the $W_3$ ones constructed by Bowcock and Watts. We find connection between quantum Toda models and the fusion method.Comment: 8 pages, LaTeX, ITP Budapest 50

On the number of instabilities of cosmological solutions in an Einstein-Yang-Mills system

A detailed numerical stability analysis of the static, spherically symmetric globally regular solutions of the Einstein-Yang-Mills equations with a positive cosmological constant, Lambda, is carried out. It is found that the number of unstable modes in the even parity sector is n for solutions with n=1,2 nodes as Lambda varies. The solution with n=3 nodes exhibits a rather surprising behaviour in that the number of its unstable modes jumps from 3 to 1 as Lambda crosses (from below) a critical value. In particular the topologically 3-sphere type solution with n=3 nodes has only a single unstable mode.Comment: minor corrections,to appear in Physics Letters

Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients

The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we derive analytic ready-to-use first post-Newtonian eccentric waveform in Fourier domain with the use of Hansen coefficients. Introducing generic perturbations of celestial mechanics we have generalized the Hansen expansion to the first post-Newtonian order which are then used to express the waveforms. Taking into account the high eccentricity of the orbit leads to the appearance of secular terms in the waveform which are eliminated with the introduction of a phase shift. The waveforms have a systematic structure and as our main result these are expressed in a tabular form.Comment: 19 pages, 3 figure