Supersymmetric rotating black holes and causality violation

Abstract

The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us to obtain the Stäckel-Killing tensor. We use these facts to give the maximal analytic extension of the spacetime and discuss some aspects of its causal structure. In particular, we exhibit a 'repulson'-like behaviour occuring when there are naked closed timelike curves. In this case we find that the spacetime is geodesically complete (with respect to causal geodesics) and free of singularities. When a partial Cauchy surface exists, we show, by solving the Klein-Gordon equation, that the absorption cross-section for massless waves at small frequencies is given by the area of the hole. At high frequencies a dependence on the angular quantum numbers of the wave develops. We comment on some aspects of 'inertial time travel' and argue that such time machines cannot be constructed by spinning up a black hole with no naked closed timelike curves. *

SupersymmetricAdS5black holes

“…Small charge black holes are small, with low angular momentum and almost round horizons whereas large charge black holes are large with high angular momentum and very squashed horizons. The causal structure of our solutions is very similar to that of the black holes of the ungauged theory, which was analyzed in [36]. Behind the horizon there is a naked singularity surrounded by a region of closed timelike curves.…”

The slowly rotating near extremal D1–D5 system as a ‘hot tube’

“…In that case the incident wave could be absorbed at the conical defect and possibly return with some knowledge of the quantum state at the defect. (A similar reflection from the singularity for a different rotating system was studied in [11]). …”

Time Travel and Time Machines

“…75 BMPV black holes are the supersymmetric counterparts of the Kerr-Newman black holes of GR: they are charged, rotating black holes in simply connected, asymptotically flat spacetime. And similarly to the Kerr-Newman case in GR, as Gibbons and Herdeiro (1999) have shown, it can be maximally analytically extended to contain a region with CTCs. 76 Below the critical value of angular momentum, we find a black hole with an event horizon, and CTCs in a region screened off by this horizon from asymptotic observers (Gauntlett et al 2003, 4589).…”

“…40 The spacetime then has topology R × Σ, where the topology of the three-spaces Σ t is arbitrary but must be the same for all Σ t . 41 Conversely, however, not every spacetime with topology R × Σ automatically 39 The qualification is essential, for if one neglects gauge freedom then the initial data appear to underdetermine the dynamical evolution -the solution is only fixed up to diffeomorphism. Furthermore, the initial data for GR must satisfy constraints.…”

“…40 We thus assume that the spacetimes at stake afford a time orientation, and that this time orientation is encoded in the global time function. 41 At least for spatially compact Hausdorff spacetimes M, g ab ; this is essentially Geroch's Theorem (Geroch 1967) which states that for a compact spacetime M, g ab whose boundary is the disjoint union of two closed spacelike affords a global time function or a Cauchy surface. As a matter of fact, the spacetime may be foliated using a "flow of space" rather than a "flow in time."…”