![]() We analyze vacuum polarization and quadratic fluctuations. We study the energy-momentum tensor of the string and compute the exact expectation values of all its components. We compute the exact expectation values of the total number (N) and mass (M2) operators and show that they are finite, which generalize our previous results in the Aichelburg–Sexl geometry. We do all the treatment for a general shock wave space–time of any localized source. This throws light on the rôle of the space–time geometry in this problem. We investigate at the quantum level the nonlinear transformation relating the string operators (zero modes and oscillators) and Fock space states before and after the collision with gravitational shock waves. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct nonsingular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation. The sign of the scalar curvature is changed by the quantum corrections in oscillating cosmologies and evolves with time in the nonoscillating cases. We analyze these cosmologies in detail with respect to the behavior of the scale factors, the scalar curvature, and the string coupling. In both two and three dimensions, we construct nonsingular oscillating cosmologies, nonsingular expanding and inflationary cosmologies including a de Sitter (exponential) stage with a positive scalar curvature as well as nonsingular contracting and deflationary cosmologies. However, considering different patches of the global manifolds allows the construction of nonsingular spacetimes with a cosmological interpretation. All semiclassical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. ![]() Nonsingular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). ![]() ![]() This phenomenon has no analogue in flat spacetime and follows to the coupling of the strings with the geometry.įinally, the string dynamics next and inside a Schwarzschild black hole is analyzed and their physical properties discussed. That is, a single world-sheet simultaneously describes many different and independent strings. Multistring solutions are a new feature in curved spacetimes. We report on the exact integrability of the string equations plus the constraints in de Sitter spacetime that allows to systematically find exact string solutions by soliton methods and the multistring solutions. The self-consistent string solution exhibits the realistic matter dominated behaviour R ≃ TĢ/3 for large time:- and the radiation dominated behaviour R ≃ Tġ/2 for early times (T being the cosmic time). The energy-momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is derived. Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. (In Minkowski spacetime, all string solutions arc of the stable type). For stable strings, the energy and proper size arc bounded. For the dual to unstable strings, the energy and size blow up for R → 0 as 1/R. For the unstable strings, the energy and size grow for large scale factors R → ∞, proportional to R. Three different types of behaviour appear: unstable, dual to unstable and stable. The classical behaviour of strings in FRW and inflationary spacetimes is now understood in a large extent from the various types of explicit string solutions. That is, the string perturbation approach, the null string approach, the τ-expansion, and the construction of global solutions (for instance by inverse scattering methods). The different methods available to solve the string equations of motion and constraints in curved spacetimes are described. The string dynamics in cosmological and black hole spacetimes is investigated. Recent progress on string theory in curved space times is reviewed.
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