Abstract
It was recently observed that Kerr-AdS metrics with negative mass can describe smooth spacetimes that have a region within which naked closed time-like curves can arise, 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 asymptotic time coordinate be periodic, with precisely the same period as that which arises naturally for the global AdS, viewed as a hyperboliod in one extra dimension, 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 solutions can be embedded in gauged supergravity, they will be supersymmetric. We also compare the global structure of the BPS AdS3 time machine with the BTZ black hole, and show that the global structure allows two different supersymmetric limits.
Highlights
As well as having non-zero mass and possibly rotation
It was recently observed that Kerr-AdS metrics with negative mass can describe smooth spacetimes that have a region within which naked closed time-like curves can arise, bounded by a velocity of light surface
We study the relation between the time machine and the BTZ spacetimes, and compare their Killing spinors in the respective BPS limits
Summary
The metric, satisfying Rμν = −(D − 1)g2gμν, contains two integration constants (m, a), and it is given by [27]. Where Ξ = 1 − a2g2, and dΣ2n−1 is the standard Fubini-Study metric on CPn−1. There is circle, parameterised by the coordinate ψ with period 2π, which is fibred over the CPn−1 base, and σ is the 1-form on the fibres, given by σ = dψ + A with dA = 2J where J is the Kahler form on CPn−1. The terms (σ2 + dΣ2n−1) in the metric are nothing but the metric. It will be helpful to make a coordinate transformation and a redefinition of the integration constants to replace (m, a) by (μ, ν), as follows: r2 + a2 → r2 , Ξ ν a= , μ. The metric (2.5) describes a rotating black hole if μ and ν are both positive, and a time machine if μ and ν are both negative [13], as we shall review later
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