Retrieving black hole information from the main Lorentzian saddle point

TL;DR

This paper demonstrates that by carefully applying the steepest descent method to the classical saddle point in black hole backgrounds, one can transform the expected exponential decay of correlation functions into a late-time growth, supporting information retrieval.

Contribution

It shows that the late-time growth of correlation functions can be derived from the main saddle point without additional configurations, providing a new perspective on the information paradox.

Findings

Late-time correlation functions grow, indicating information retrieval.

The ramp in the two-point function is analytically derived in JT gravity.

No need for subdominant configurations to explain the ramp.

Abstract

One of the most striking evidences of the information loss paradox is that, according to the Hawking's calculation, the correlation functions of a test scalar field exponentially decay in time. In this paper, I argue that a judicious use of the steepest descent expansion on the classical saddle point (the Black Hole background), is enough to change this early time decay into a late time growing, in agreement with information retrieval. I will explicitly show this in the Jackiw-Teitelboim gravity. There, the so-called "ramp" in the bulk tow-point function, is analytically obtained without the need of any other subdominant configurations of the gravity path integral.