Geometric Horizon Inflation: An Effective Field Theory for Binary Black Hole Mergers in an Isometric Tensor Network

The Hawking Area Theorem states that a black hole horizon area cannot de-

crease. Current gravitational wave observations confirm this constraint to within

∼10%. Discrete quantum gravity models suggest the continuum approximation of

General Relativity fails at the horizon. In this paper, we construct an Effective Field

Theory (EFT) using the Selection-Stitch Model (SSM). We model the vacuum as an

Isometric Tensor Network (isoTNS) on a saturated Face-Centered Cubic (K = 12)

lattice. We write the explicit lattice strain action SisoTNS and perform the complete

functional variation δS/δgµν to derive the stress-energy tensor Tµν at the horizon.

We establish consistency with the Israel-Darmois thin-shell junction conditions by

computing the extrinsic curvature discontinuity [Kij] across the horizon shell. The

area inflation is derived from the Raychaudhuri equation with the modified source

term, yielding a scale-invariant band of ∆A ≈ 6.86−7.13%. We compute the

quasinormal mode (QNM) frequency shift for the dominant (2,2,0) mode using per-

turbation theory on the Teukolsky equation: δω/ω=−ϵ/2 =−3.4%. For a 100M⊙

remnant, this produces a ringdown frequency decrease of 4−6 Hz and a damping

time increase of∼3.5%. These shifts match GW250114 parameter estimations and

sit within the projected sensitivity of upcoming XG observatories.