STRING DYNAMICS IN COSMOLOGICAL AND BLACK-HOLE BACKGROUNDS - THE NULLSTRING EXPANSION

We study the classical dynamics of a bosonic string in the D-dimension al flat Friedmann-Robertson-Walker and Schwarzschild backgrounds. We m ake a perturbative development in the string coordinates around a null string configuration; the background geometry is taken into account e xactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge worl d-sheet tau coordinate is given by X(0)(sigma,tau)=q(sigma)tau(1/(1+2 beta))+c(2)B(0)(sigma,tau)+..., B-0(sigma,tau)=Sigma(k)b(k)(sigma)tau( k) where q(sigma) is a function of the momentum component P-0(sigma), b(k)(sigma) are obtained from the equation for the first order fluctua tions, and beta is the exponent of the conformal factor in the Friedma nn-Robertson-Walker metric, i.e., R similar to eta(beta). The string p roper size, at first order in the fluctuations, grows such as the conf ormal factor R(eta) 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 tim e coordinates (r,phi,t) are r=Sigma(n)A(n)(1)(sigma)(-tau)(2n/(D+1)), phi=Sigma(n)A(n)(3)(sigma)(-tau)((D-5+2n)/(D+1)), and t=Sigma(n)A(n)(0 )(sigma)(-tau)(1+2n(D-3)/(D+1)). The first terms of the series represe nt a generic approach to the Schwarzschild singularity at r=0. First a nd higher order string perturbations contribute with higher powers of tau. The integrated string energy-momentum tensor corresponds to that of a null fluid in D-1 dimensions. As the string approaches the r=0 si ngularity its proper size grows indefinitely such as similar to(-tau)( -(D-3)/(D+1)). We end the paper giving three particular exact string s olutions inside the black hole. They represent, respectively, straight strings across the origin, twisted, and rigidly rotating strings.