Bulk Spacetime Encoding via Boundary Ambiguities

TL;DR

This paper introduces an analytical method to reconstruct the metric and its derivatives at black hole horizons using boundary Green's function ambiguities, revealing universal identities among pole-skipping points.

Contribution

It provides a fully analytical, linear-equation-based approach to horizon reconstruction and uncovers universal polynomial constraints among pole-skipping points, independent of bulk details.

Findings

Reconstruction of horizon metric and derivatives from pole-skipping points.

Identification of universal polynomial constraints among pole-skipping points.

Method applicable to various black hole geometries and dimensions.

Abstract

We propose a method to reconstruct the metric and its arbitrary-order derivatives at the horizon for any static, planar-symmetric black hole, using an infinite set of discrete pole-skipping points in momentum space where the boundary Green's function becomes ambiguous. This method is fully analytical and involves solving only linear equations. The near-horizon reconstruction can extend either inside or outside the horizon until reaching the nearest singularity in the complex radial plane. It further enables a reinterpretation of any pure gravitational field equation in pole-skipping data. Moreover, our method reveals that the pole-skipping points are redundant: only a subset is independent, while the rest are fixed by an equal number of homogeneous polynomial constraints. These identities are universal, independent of the details of the bulk geometry, including its dimensionality, asymptotic behavior, or the existence of a holographic duality.