Boundary Response Analysis and the Near-Horizon Scrambling Brane: Diagnosing Dissipative Structure at the Horizon Scale

Abstract

We introduce Boundary Response Analysis (BRA), a three-channel diagnostic framework for testing whether compact objects possess classical event horizons or dissipative near-horizon boundary layers, together with a concrete minimal realization: the four-parameter Near-Horizon Scrambling Brane (NHSB) model. The NHSB model deforms standard binary black hole (BBH) waveform templates through three observational channels — conservative tidal dephasing, dissipative heating, and modified ringdown structure — connected through a unified response-kernel parameterization. The model is parameterized by a compactness offset ε, a conservative response amplitude Λ★, a brane absorptivity A, and a scrambling exponent δ, and is designed to probe the almost-black-hole corner of parameter space. We anchor the constitutive laws to a minimal causal, passive response kernel χ(ω) = χ₀/[1 + (iωτ)^δ], from which both reactive and dissipative sectors descend as real and imaginary parts. We validate the framework through synthetic injection studies, mismatched-model bias tests confirming the single-δ closure is safe (bias ≤ 0.4σ across all cases), and a proof-of-concept analysis of four public GWOSC events (GW150914 and three O4a detections). All three clean events are consistent with the BBH null hypothesis, with prior-dominated Λ★ posteriors confirming the channel hierarchy on real detector noise. A source-marginalized Bayesian event-level analysis on GW150914, comparing BBH, tidal-only, heating-only, and BRA/NHSB models, shows that the dissipative channel becomes data-informed (σ(A) = 0.15, narrower than the prior width) while the conservative channel remains prior-dominated — the first demonstration of the BRA channel hierarchy under source-parameter marginalization. A sensitivity-timeline analysis demonstrates that the dissipative heating channel reaches informative sensitivity for the "boundary or no boundary" question before either echoes or conservative tidal effects, because heating accumulates coherently over the full inspiral–merger waveform. The BRA framework and NHSB model are intended as a structured, falsifiable diagnostic for organizing tests of the "no entry versus no return" distinction at the horizon scale with current and next-generation gravitational-wave detectors.

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