22 Gravitational-Wave Ringdown Test

Beyond galactic dynamics, the informational framework makes concrete predictions for strong-gravity phenomena. In particular, it predicts small but systematic deviations from general relativity in the ringdown phase of black-hole mergers. These deviations arise from horizon-scale suppression of information propagation and provide an independent observational test.

22.1 Horizon-Scale Information Suppression

As discussed in Sections 15 and 16, black holes correspond to regimes in which the effective diffusion coefficient tends to zero:

Near the horizon, informational propagation is therefore strongly suppressed. While spacetime geometry remains an excellent approximation outside the horizon, this suppression alters the boundary conditions governing perturbations.

Importantly, no hard reflective surface or exotic structure is introduced. The modification arises smoothly from the same informational dynamics responsible for horizon formation.

22.2 Modified Quasinormal Modes

In general relativity, the ringdown phase is described by a discrete set of quasinormal modes with frequencies $\omega_n^{\mathrm{GR}}$ determined solely by the black-hole mass and spin.

Within the informational framework, horizon-scale suppression modifies the effective potential governing perturbations. To leading order, this produces a small shift in the mode frequencies:

where:

• $a_{\mathrm{hor}}$ is the characteristic acceleration at the horizon,
• $a_{\ast}$ is the universal acceleration scale extracted from galactic dynamics,
• $\epsilon$ and $p$ are order-unity constants determined by the suppression profile.

With the ratio written as $a_{\mathrm{hor}}/a_\ast$ above (corrected from an earlier version that inverted this ratio), the suppression term vanishes as $a_{\mathrm{hor}}/a_\ast\to0$ (ordinary stellar/intermediate-mass black holes, matching the expectation that deviations are negligible there) and grows as $a_{\mathrm{hor}}\to a_\ast$ (high-mass black holes), consistent with Section 23.1's claim that deviations increase with mass.

22.3 Expected Magnitude of Deviations

For stellar-mass and intermediate-mass black holes, the predicted fractional deviations in the dominant ringdown frequencies are of order:

These deviations are too small to affect inspiral dynamics or current weak-field tests. They are confined to the late-time ringdown regime, where horizon-scale physics dominates.

Crucially, the magnitude of the deviation is controlled by the same acceleration scale $a_{\ast}$ that appears in galactic dynamics. No new parameters are introduced.

22.4 Current and Future Detector Sensitivity

Current gravitational-wave detectors (LIGO, Virgo, KAGRA) are approaching the sensitivity required to constrain percent-level deviations in ringdown modes, though definitive detection remains challenging.

Next-generation detectors, including the Einstein Telescope, Cosmic Explorer, and LISA, are expected to achieve sufficient signal-to-noise ratios to resolve sub-percent deviations in multiple quasinormal modes.

A confirmed deviation consistent with the predicted suppression pattern would provide strong evidence for the informational framework. Conversely, the absence of such deviations within experimental sensitivity would falsify the theory cleanly.

With two independent observational tests established, we now synthesize the results and discuss their implications for the foundations of physics.