Ringdown of a Bounced Core: Quasi-Normal Modes and Echoes of a Merger Remnant in the Aldred Frame

In Einstein-Cartan spin-torsion gravity with the Aldred Limit rho_A = 9.72e54 g/cm^3, collapse halts and reverses at rho_A, so a binary merger remnant contains a bounced core rather than a singularity. The bounced core of a merger remnant sits at R_A(M) = [3M/(4 pi rho_A)]^(1/3) = 1.45e-7 cm for a 62 solar-mass remnant, a fraction R_A/r_s = 7.90e-15 of its Schwarzschild radius: deep inside the horizon. The frame's configuration therefore has a Kerr exterior, a fundamental (2,2,0) quasi-normal mode identical to Kerr (zero deviation in frequency and damping time; 248.4 Hz and 4.06 ms for a GW150914-like remnant of detector-frame mass 68 solar masses and spin 0.67, against the measured 251 +/- 8 Hz and 4.0 +/- 0.3 ms), and zero observable echoes at any amplitude. The horizonless reflective configuration that published echo searches test is a different object: a surface at the horizon would require a mean interior density of 4.79e12 g/cm^3, a factor 2.03e42 below rho_A. Priced in full, that configuration has an echo delay of 0.123 s (Schwarzschild tortoise) to 0.288 s (spinning estimate) at 68 solar masses for a Planck-scale surface offset, cavity resonances spaced by 8.10 Hz with damping times of 103-1172 ms, and 2, 3, or 5 echoes above a strain floor of 2e-23 for per-echo survival factors of 0.3, 0.5, and 0.7 at a first-echo amplitude of 10 percent of the ringdown peak. Published searches find no echoes in O1-O3 and constrain GW150914 echo amplitudes to roughly 15 percent of the merger amplitude; those results constrain and at high reflectivity exclude the near-horizon configuration, but cannot touch the frame's configuration, whose prediction is the reported null. A confirmed echo train or a confirmed non-zero quasi-normal-mode deviation from Kerr would falsify the frame's configuration. All numbers are produced by the deposited compute.py. AI-use disclosure: this paper was drafted and computed with the assistance of Dave, an AI assistant operated by Aldred Industries, under the direction of the author; all derivations, computations, and conclusions were reviewed against the frame's equations before deposit.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-10
DOI
https://doi.org/10.5281/zenodo.24110770
Primary Topic
Pulsars and Gravitational Waves Research
Type
preprint
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preprint

Ringdown of a Bounced Core: Quasi-Normal Modes and Echoes of a Merger Remnant in the Aldred Frame

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Pulsars and Gravitational Waves Research
preprint

Ringdown of a Bounced Core: Quasi-Normal Modes and Echoes of a Merger Remnant in the Aldred Frame

William Alexander Aldred
preprint en

Abstract

In Einstein-Cartan spin-torsion gravity with the Aldred Limit rho_A = 9.72e54 g/cm^3, collapse halts and reverses at rho_A, so a binary merger remnant contains a bounced core rather than a singularity. The bounced core of a merger remnant sits at R_A(M) = [3M/(4 pi rho_A)]^(1/3) = 1.45e-7 cm for a 62 solar-mass remnant, a fraction R_A/r_s = 7.90e-15 of its Schwarzschild radius: deep inside the horizon. The frame's configuration therefore has a Kerr exterior, a fundamental (2,2,0) quasi-normal mode identical to Kerr (zero deviation in frequency and damping time; 248.4 Hz and 4.06 ms for a GW150914-like remnant of detector-frame mass 68 solar masses and spin 0.67, against the measured 251 +/- 8 Hz and 4.0 +/- 0.3 ms), and zero observable echoes at any amplitude. The horizonless reflective configuration that published echo searches test is a different object: a surface at the horizon would require a mean interior density of 4.79e12 g/cm^3, a factor 2.03e42 below rho_A. Priced in full, that configuration has an echo delay of 0.123 s (Schwarzschild tortoise) to 0.288 s (spinning estimate) at 68 solar masses for a Planck-scale surface offset, cavity resonances spaced by 8.10 Hz with damping times of 103-1172 ms, and 2, 3, or 5 echoes above a strain floor of 2e-23 for per-echo survival factors of 0.3, 0.5, and 0.7 at a first-echo amplitude of 10 percent of the ringdown peak. Published searches find no echoes in O1-O3 and constrain GW150914 echo amplitudes to roughly 15 percent of the merger amplitude; those results constrain and at high reflectivity exclude the near-horizon configuration, but cannot touch the frame's configuration, whose prediction is the reported null. A confirmed echo train or a confirmed non-zero quasi-normal-mode deviation from Kerr would falsify the frame's configuration. All numbers are produced by the deposited compute.py. AI-use disclosure: this paper was drafted and computed with the assistance of Dave, an AI assistant operated by Aldred Industries, under the direction of the author; all derivations, computations, and conclusions were reviewed against the frame's equations before deposit.

Zenodo (CERN European Organization for Nuclear Research)
Pulsars and Gravitational Waves Research
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