Singularities and Closed String Tachyons

A basic problem in gravitational physics is the resolution of spacetime singularities where general relativity breaks down. The simplest such singularities are conical singularities arising from orbifold identifications of flat space, and the most challenging are spacelike singularities inside black holes (and in cosmology). Topology changing processes also require evolution through classically singular spacetimes. I briefly review how a phase of closed string tachyon condensate replaces, and helps to resolve, basic singularities of each of these types. Finally I discuss some interesting features of singularities arising in the small volume limit of compact negatively curved spaces and the emerging zoology of spacelike singularities. Based on comments at the 23rd Solvay conference in physics. 1 Singularities and Winding Modes In the framework of string theory, several types of general relativistic singularities are replaced by a phase of closed string tachyon condensate. The simplest class of examples involves spacetimes containing 1-cycles with antiperiodic Fermion boundary conditions. This class includes spacetimes which are globally stable, such as backgrounds with late-time long-distance supersymmetry and/or AdS boundary conditions. In the presence of such a circle, the spectrum of strings includes winding modes around the circle. The Casimir energy on the worldsheet of the string contributes a negative contribution to the mass squared, which is of the form