Black Holes, Shock Waves, and Causality in the AdS/CFT Correspondence

TL;DR

This paper explores the AdS/CFT correspondence by relating gravitational shock waves in AdS to light cone states in the CFT, providing insights into causality and the energy-momentum tensor behavior.

Contribution

It establishes a detailed connection between gravitational shock waves and light cone states in the CFT, advancing understanding of causality in AdS/CFT.

Findings

Gravitational shock waves in AdS correspond to localized light cone states in the CFT.

The CFT reproduces causal relations observed in AdS through these shock wave and light cone state mappings.

The approach offers a new method to test causality within the AdS/CFT framework.

Abstract

We find the expectation value of the energy-momentum tensor in the CFT corresponding to a moving black hole in AdS. Boosting the black hole to the speed of light, keeping the total energy fixed, yields a gravitational shock wave in AdS. The analogous procedure on the field theory side leads to ``light cone'' states, i.e., states with energy-momentum tensor localized on the light cone. The correspondence between the gravitational shock wave and these light cone states provides a useful tool for testing causality. We show, in several examples, how the CFT reproduces the causal relations in AdS.