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June 26, 2026Open Access

Equally Spaced Black Hole Echo Harmonics from S³ Topological Eigenspectrum with Supplementary Derivations and Observational Test Specifications

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QZQ Zhao

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Overview

Randomized trial identifies equal-spacing versus unequal-spacing in black hole echo frequencies, highlighting their significance.

Key Points

  • This research aims to distinguish black hole gravitational-wave echo models based on harmonic frequency spacing.
  • Identified a binary observational discriminant for echo models
  • Analyzed S3 topological resonance to derive eigenspectrum spacing
  • Provided specifications for observational tests using LISA and ground-based detectors.
  • Equal-spacing predicted by S3 topological resonance (fn=n·f0)
  • Mainstream models predict unequal-spacing due to various gravitational theories
  • Future observations can confirm model predictions by detecting resolvable harmonics.

Cite This Study

Q Zhao (2026) studied this question.

synapsesocial.com/papers/6a3e1907030ad1a9b3091e50https://doi.org/10.5281/zenodo.20822417
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