Circular String-Instabilities in Curved Spacetime

Abstract

We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loustó and Sánchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordström and de Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow infinitely for $r\to 0$ (ring-collapse), while the "angular" perturbations are bounded in this limit. For $r\to \infty$ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loustó and Sánchez who considered perturbations around the string center of mass.

24 pages Latex + 2 figures (not included). Observatoire de Paris, Meudon No. 93052

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• Exact String Solutions in Nontrivial Backgrounds
• Null string evolution in black hole and cosmological spacetimes
• The evolution of cosmic string loops in Kerr-de Sitter spacetimes
• String Spreading on Black Hole Horizon
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• Cosmic strings in a space-time with positive cosmological constant
• Null Strings in Kerr Spacetime
• Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process
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• Quantum Field Theory Analysis of Polarizations Correlations, Entanglement and Bell's Inequality: Explicit Processes
• Advances in String Theory in Curved Backgrounds: A Synthesis Report
• The circular loop equation of a cosmic string with time-varying tension
• Stable and Unstable Circular Strings in Inflationary Universes
• Strings Next To and Inside Black Holes
• The circular loop equation of a cosmic string with time-varying tension in de Sitter spacetimes
• Pulsating string solution and stability in two parameter $\chi$-deformed background