STRING DYNAMICS IN COSMOLOGICAL AND BLACK HOLE BACKGROUNDS: THE NULL STRING EXPANSION

We study the classical dynamics of a bosonic string in the D-dimensional flat Friedmann–Robertson–Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a null string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet τ–coordinate is given by , B⁰(σ,τ) = Σ_kb_k(σ)τ^k where b_k(σ) are given by Eqs. (3.15), and β is the exponent of the conformal factor in the Friedmann–Robertson–Walker metric, i.e. R ∼ η^β. The string proper size, at first order in the fluctuations, grows like the conformal factor R(η) and the string energy–momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime D generic. In the null string expansion, the radial, azimuthal, and time coordinates (r, ϕ, t) are , and . The first terms of the series represent a generic approach to the Schwarzschild singularity at r = 0. First and higher order string perturbations contribute with higher powers of τ. The integrated string energy-momentum tensor corresponds to that of a null fluid in D – 1 dimensions. As the string approaches the r = 0 singularity its proper size grows indefinitely like ∼ (−τ)^{−(D−3)/(D+1)}. We end the paper giving three particular exact string solutions inside the black hole. They represent respectively straight strings across the origin, twisted, and rigidly rotating strings.