Causality Violation and Naked Time Machines in AdS_5

TL;DR

The paper analyzes supersymmetric charged rotating AdS$_5$ black holes and exposes closed timelike curves outside the event horizon, a property that persists when lifted to rotating D3-brane solutions in ten dimensions. By studying the horizon structure through the zeros of a sixth-degree polynomial in a dimensionless radius and examining geodesics and quantum scattering, it demonstrates exterior geodesic completeness and a vanishing Klein-Gordon absorption cross section, hinting at a zero effective temperature. A holographic perspective links bulk chronology protection to unitarity bounds in the boundary $N=4$, $D=4$ super Yang–Mills theory, and the paper shows that CTCs can be resolved or altered under higher-dimensional lifting, complicating the bulk-boundary causality-unitarity relationship. Overall, these results illuminate the intricate connection between causality, horizon geometry, and unitarity in AdS/CFT contexts, with implications for the interpretation of black hole thermodynamics in gauged supergravity.

Abstract

We study supersymmetric charged rotating black holes in AdS$_5$, and show that closed timelike curves occur outside the event horizon. Also upon lifting to rotating D3 brane solutions of type IIB supergravity in ten dimensions, closed timelike curves are still present. We believe that these causal anomalies correspond to loss of unitarity in the dual ${\cal N}=4$, D=4 super Yang-Mills theory, i.e. the chronology protection conjecture in the AdS bulk is related to unitarity bounds in the boundary CFT. We show that no charged or uncharged geodesic can penetrate the horizon, so that the exterior region is geodesically complete. These results still hold true in the quantum case, i.~e.~the total absorption cross section for Klein-Gordon scalars propagating in the black hole background is zero. This suggests that the effective temperature is zero instead of assuming the naively found imaginary value.