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Researchers developed an analytical method to reconstruct black hole properties at the horizon using pole-skipping points. This approach simplifies gravitational field equations and reveals universal constraints on black hole geometry.

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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.