Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions

Abstract

The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\ne 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto S$ for large $S$. For an oscillating string $(0\le S\le S_{max})$, the average energy $<E>$ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.

32 pages, Latex file, figures available from the authors under request. LPTHE-PAR 93-56

References in corpus (1)

• Exact String Solutions in 2+1-Dimensional De Sitter Spacetime

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