Constraining Black Hole Horizon Properties Through Long-Duration Gravitational Wave Observations

TL;DR

This work tests the Kerr black-hole horizon by searching for long-lived, near-horizon quasinormal modes that arise if a reflective surface exists at a small offset $\epsilon$ from the horizon. It develops a long-duration Bayesian framework to fit a damped sinusoid post-merger signal, applied to GW150914, 18 additional LVK events, three high-SNR O4a events, and the high-SNR O4b event GW250114. By combining posterior samples across events, it obtains a joint bound of $\log_{10}\epsilon < -27.12$, while the strongest single-event bound from GW250114 is $\log_{10}\epsilon < -29.58$, pushing tests to Planck-scale horizon deformations. The results show no detectable deviations from Kerr, reinforcing the classical black-hole paradigm and demonstrating the power of population-level inference for probing near-horizon physics with gravitational waves.

Abstract

We perform a long-duration Bayesian analysis of gravitational-wave data to constrain the near-horizon geometry of black holes formed in binary mergers. Deviations from the Kerr geometry are parameterized by replacing the horizon's absorbing boundary with a reflective surface at a fractional distance epsilon. This modification produces long-lived monochromatic quasinormal modes that can be probed through extended integration times. Building on previous work that set a bound of log10(epsilon) = -23.5 for GW150914, we reproduce and validate those results and extend the analysis to additional events from the LIGO-Virgo-KAGRA observing runs. By combining posterior samples from multiple detections, we construct a joint posterior yielding a tightened 90 percent upper bound of log10(epsilon) < -27.12, demonstrating the statistical power of population-level inference through cumulative evidence. Finally, analyzing the newly observed high signal-to-noise ratio event GW250114 from the O4b run, we obtain the most stringent single-event constraint to date, log10(epsilon) < -29.58 (90 percent credible region). Our findings provide the strongest observational support to date for the Kerr geometry as the correct description of post-merger black holes, with no detectable horizon-scale deviations.

Figures (9)

• Figure 1: The figure compares the behavior of GWs in black holes and UCOs. In BHs, infalling GWs are fully absorbed at the horizon, leaving no reflection. In contrast, for UCOs the GWs are weakly interacting, and reemerge after a delay due to partial reflection from a surface just outside the would-be horizon. This delayed re-emission is caused by the high gravitational redshift near the surface. This property is used during the post-merger ringdown to examine the presence or absence of a horizon.
• Figure 2: Top panel: The boundary conditions that govern wave propagation in black hole spacetime. Bottom panel: The reflecting conditions for waves outside an UCO. Figure taken from boundary
• Figure 3: Posterior distribution of $\log _{10} \epsilon$ for GW150914. Shaded regions indicate probability density; dashed lines mark $50\%$ and $90\%$ credible intervals. The leftmost hatched region corresponds to Planckian scales (the Planck length from the classical horizon $\sim 10^{-35}m$ shown in the top axis). The posterior exhibits the same qualitative behavior observed across all analyzed events — a peak near the Kerr horizon and a rapid decay toward larger $\epsilon$ values.
• Figure 4: Posterior distribution of $\log _{10} \epsilon$ for GW$200129$. Shaded regions indicate probability density; dashed lines mark $50\%$ and $90\%$ credible intervals. The leftmost hatched region corresponds to Planckian scales (the Planck length from the classical horizon $\sim 10^{-35}m$ shown in the top axis). The posterior exhibits the same qualitative behavior as previously observed for GW150914.
• Figure 5: Scatter plots comparing the obtained upper bounds on $\epsilon$ to the SNR of each event. Left: Bound vs. simulated ringdown SNR. Right: Bound vs. full-merger SNR. For each event, two linked markers are shown — one for the simulated ringdown SNR and one for the full-merger SNR — and each pair is labeled with the event name. Events with higher SNRs provide tighter bounds, moving upward toward smaller values of $\epsilon$. The left panel shows a wider scatter at low simulated SNRs, indicating that noise dominates the bound determination in those cases.