Causality Violation and Naked Time Machines in AdS_5

TL;DR

This paper investigates supersymmetric charged rotating black holes in AdS_5, revealing closed timelike curves outside the horizon and exploring their implications for unitarity in the dual super Yang-Mills theory, with findings on geodesic completeness and quantum effects.

Contribution

It demonstrates the presence of causality violations in AdS_5 black holes and connects these anomalies to unitarity bounds in the dual CFT, extending the analysis to quantum regimes.

Findings

Closed timelike curves exist outside the event horizon.

No geodesic can penetrate the horizon, ensuring exterior geodesic completeness.

Quantum analysis shows zero absorption cross section, implying zero effective temperature.

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.