A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory

TL;DR

This paper surveys the status of time-dependent string theory backgrounds with space-like singularities, outlining both perturbative and non-perturbative approaches. It highlights key ideas such as BKL cosmological dynamics, worldsheet analyses of Misner space, and tachyon condensation, as well as holographic and matrix-model perspectives provided by AdS/CFT and M(atrix) theory. The discussion emphasizes partial progress toward understanding singularities, including potential smoothing mechanisms and the limitations of current methods. Overall, the work maps a landscape of stringy cosmologies and identifies avenues where holography and non-perturbative dynamics offer insights into the interiors behind horizons and the fate of spacelike singularities.

Abstract

These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.

Figures (8)

• Figure 1: Penrose diagram for the Kruskal extension of the Schwarzschild black hole, showing conformal infinity as well as the two singularities.
• Figure 2: The AdS$_d$, $d>3$, eternal black hole, the causal structure is similar to the Schwarzschild black hole only with the asymptotic boundary changed.
• Figure 3: The Minkowski space time (on the left) is divided into 4 region by the action of the boost orbifold. The dotted lines are the boundaries of the orbifold's fundamental region, and are identified. The boost orbifold geometry (on the right) is that of 4 cones. Each quadrant of Minkowski spacetime is mapped in the orbifold to one of the orbifold's cones.
• Figure 4: Minkowski space is divided by the shifted boost orbifold into 6 regions (seen at a fixed X cross section). The dashed curves is where $\hat{\zeta}^2=0$.
• Figure 5: The geometry of the BTZ black hole (with no angular momentum) as seen from two different cross section. The cross-section on the right is the same viewpoint described earlier (figure \ref{['adsbh']}) where we see the outside the horizon area (1,1') including the asymptotic boundary, the singularities and the inner horizon area's (2,2'). In the cross-section on the left we see the inner horizon areas (2,2') but also the behind the singularity areas (3,3')