Three lessons in causality : what string theory has to say about naked singularities, time travel and horizon complementarity

Abstract

We begin by presenting some results of studying certain axially symmetric super- gravity geometries corresponding to a distribution of BPS D6-branes wrapped on K3, obtained as extremal limits of a rotating solution. The geometry's unphysical regions resulting from the wrapping can be repaired by the enhancon mechanism, with the result that there are two nested enhancon shells. For a range of parameters, the two shells merge into a single toroidal surface. Given the quite intricate nature of the geometry, it is an interesting system in which to test previous techniques that have been brought to bear in spherically symmetric situations. We are able to check the consistency of the construction using supergravity surgery techniques, and probe brane results. Implications for the Coulomb branch of (2+1)-dimensional pure SU(N) gauge theory are extracted from the geometry. Related results for wrapped D4-- and D5-brane distributions are also discussed. Next, we turn to the issue of time travel. Many solutions of General Relativity appear to allow the possibility of time travel. This was initially a fascinating discovery, but geometries of this type violate causality, a basic physical law which is believed to be fundamental. Although string theory is a proposed fundamental theory of quantum gravity, geometries with closed timelike curves have resurfaced as solutions to its low energy equations of motion. In chapter 3, we will study the class of solutions to low energy effective supergravity theories related to the BMPV black hole and the D1--D5-brane-SSW system. Time travel appears to be possible in these geometries. We will attempt to build the causality violating regions and propose that stringy effects prohibit their construction.

(cont.) We will show how the geometry is corrected and that, once corrected, causality is preserved. We will track our chronology protection proposal in the dual conformal field theory. The absence of closed timelike curves in the geometry coincides with the preservation of unitarity ill the conformal field theory. Our mechanism will also have the pleasing result of being an enforcer of the second law of thermodynamics. We will generalize our results to a broader class of geometries. Finally we discuss physics associated with horizons. A de Sitter Space version of Black Hole Complementarity is formulated which states that an observer in de Sitter Space describes the surrounding space as a sealed finite temperature cavity bounded by a horizon which allows no loss of information. We then discuss the implications of this for the existence of boundary correlators in the hypothesized dS/CFT correspondence. We find that dS complementarity precludes the existence of the appropriate limits. We find that the limits exist only in approximations in which the entropy of the de Sitter Space is infinite. The reason that the correlators exist in quantum field theory in the de Sitter Space background is traced to the fact that horizon entropy is infinite in QFT. We will consider the implications of a cosmological constant for the evolution of the universe, under a set of assumptions motivated by the holographic and horizon complementarity principles. We discuss the "causal patch" description of spacetime required by this framework, and present some simple examples of cosmologies ...