The Godel-Schrodinger Spacetime and Stringy Chronology Protection

TL;DR

This paper constructs a novel spacetime combining Godel and Schrodinger features via the null Melvin map, explores its holographic dual, and discusses potential resolutions to its closed timelike curves through brane instabilities.

Contribution

It introduces a Godel-Schrodinger spacetime with a holographic dual on a sphere and analyzes its causal structure and stability properties.

Findings

The spacetime has closed timelike curves outside a critical radius.

A holographic screen is located inside the acausal region.

Brane instabilities suggest a mechanism to remove closed timelike curves.

Abstract

We show that the null Melvin map applied to a rotational isometry of global anti-de Sitter space produces a spacetime with properties analogous to both the Godel and Schrodinger geometries. The isometry group of this Godel-Schrodinger spacetime is appropriate to provide a holographic dual for the same non-relativistic conformal theory as the ordinary Schrodinger geometry, but defined on a sphere. This spacetime also possesses closed timelike curves outside a certain critical radius. We show that a holographic preferred screen for an observer at the origin sits at an interior radius, suggesting that a holographic dual description would only require the chronologically consistent region. Additionally, giant graviton probe branes experience repulson-type instabilities in the acausal region, suggesting a condensation of branes will modify the pathological part of the geometry to remove the closed timelike curves.