Numerical relativity analysis shows the direct wave frequency in binary black hole mergers correlates with horizon frequency only incidentally at χ_f ≈ 0.7 and has evolving damping time, making it unsuitable as a probe of remnant horizon properties or for testing Hawking's area law.
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All redshift-mode contributions to Schwarzschild black-hole ringdown waveforms vanish exactly because causality forces the source-integrated Green function to vanish on the light cone.
A gravitational-wave method infers the Kerr-equivalent horizon area from direct waves in the near-merger signal of GW250114, yielding consistency with the Kerr remnant and a new test of Hawking's area law.
Exact expressions are obtained for the direct singular part of the Teukolsky retarded Green function in Schwarzschild spacetime, including angular factors and spin-dependent transport terms for constant-radius orbits.
Homogeneous solutions and connection coefficients in the radial Teukolsky equation for Kerr black holes exhibit simple poles at Matsubara frequencies that cancel in the Green's function, along with canceling zero-frequency singularities scaling as ω^{-2l-1}.
Refined propagation prescription for quasinormal modes excited by plunging particles confirms a bounce radius at r_*=0 and yields accurate reproduction of the post-bounce oscillatory waveform component from first principles.
Orthonormal QNM analysis of GW250114 raises the significance of the first overtone of the ℓ=m=2 mode from 82.5% to 99.9% and detects no significant deviation from Kerr predictions.
The prompt response is ~1.2 times stronger than quasinormal mode excitation during inspiral and enables 99% accurate reconstruction of the full inspiral-merger-ringdown waveform when combined with other components.
Exact time-domain Green function computed for the Pöschl-Teller approximation to black-hole perturbation potentials, revealing additional early-time exponentially growing modes and a light-cone plus historical waveform decomposition.
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The Direct Wave is Not a Meaningful Test of Horizon Properties
Numerical relativity analysis shows the direct wave frequency in binary black hole mergers correlates with horizon frequency only incidentally at χ_f ≈ 0.7 and has evolving damping time, making it unsuitable as a probe of remnant horizon properties or for testing Hawking's area law.