BPS Kerr-AdS Time Machines

TL;DR

This paper investigates BPS limits of Kerr-AdS spacetimes with negative mass, revealing discretized parameters, periodic time coordinates, and supersymmetry, and compares their global structure to BTZ black holes.

Contribution

It characterizes the BPS limit of Kerr-AdS time machines, including discretization of parameters, supersymmetry conditions, and their relation to known black hole solutions.

Findings

Mass and angular momenta become discretized in the BPS limit.

Time coordinate must be periodic with the same period as global AdS.

Explicit Killing spinors are constructed for equal angular momenta in odd dimensions.

Abstract

It was recently observed that Kerr-AdS metrics with negative mass describe smooth spacetimes that have a region with naked closed time-like curves, bounded by a velocity of light surface. Such spacetimes are sometimes known as time machines. In this paper we study the BPS limit of these metrics, and find that the mass and angular momenta become discretised. The completeness of the spacetime also requires that the time coordinate be periodic, with precisely the same period as that which arises for the global AdS in which the time machine spacetime is immersed. For the case of equal angular momenta in odd dimensions, we construct the Killing spinors explicitly, and show they are consistent with the global structure. Thus in examples where the solution can be embedded in a gauged supergravity theory, they will be supersymmetric. We also compare the global structure of the BPS AdS$_3$ time machine with the BTZ black hole, and show that the global structure allows to have two different supersymmetric limits.