Bulk Spacetime Encoding via Boundary Ambiguities

Area of Science:

• Theoretical Physics
• Black Hole Physics
• Gravitational Theory

Background:

• Static, planar-symmetric black holes present complex gravitational field equations.
• Reconstructing black hole properties near the horizon is crucial for understanding their behavior.
• Pole-skipping phenomena in boundary Green's functions offer potential insights.

Purpose of the Study:

• To develop an analytical method for reconstructing black hole metrics and derivatives at the horizon.
• To utilize pole-skipping points for this reconstruction.
• To reinterpret gravitational field equations using pole-skipping data.

Main Methods:

• An infinite set of discrete pole-skipping points in momentum space is used.
• The boundary Green's function's ambiguity at these points is exploited.
• The method involves solving linear equations analytically.

Main Results:

• The metric and its arbitrary-order derivatives at the horizon can be reconstructed.
• The reconstruction extends to singularities in the complex radial plane.
• Pole-skipping points are found to be redundant, with universal polynomial constraints.

Conclusions:

• A fully analytical and efficient method for black hole horizon reconstruction is established.
• Gravitational field equations can be reinterpreted through pole-skipping data.
• Universal constraints on black hole geometry are revealed, independent of specific bulk details.