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

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) = -24 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) < -38.64, 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.

💡 Research Summary

This paper presents a comprehensive Bayesian analysis of long‑duration post‑merger gravitational‑wave (GW) data to test whether the horizons of black holes formed in binary mergers deviate from the perfectly absorbing Kerr solution. The authors parameterize possible deviations by introducing a reflective surface located a fractional distance ε outside the Kerr horizon. In the limit ε→0 the surface coincides with the horizon, reproducing the standard Kerr geometry; for finite ε the boundary condition becomes perfectly reflecting (reflection coefficient R=1), which gives rise to additional, long‑lived, nearly monochromatic quasi‑normal modes (QNMs).

Theoretical development starts from the Teukolsky equation in Kerr spacetime. By imposing a reflective boundary at r=R=r₊(1+ε) the authors derive analytic approximations for the real and imaginary parts of the dominant mode frequency. The real part is essentially the horizon’s angular velocity Ω, shifted by a term proportional to 1/ln ε, while the imaginary part (the damping rate) scales as 1/(ln ε)², leading to damping times τ∼r₊(ln ε)² that can reach thousands of seconds for ε≈10⁻²⁴. Consequently, the signal appears as a single damped sinusoid:

h(t)=A e^{-(t−t₀)/τ} sin