Geometric Horizon Inflation: A Universal Prediction for Binary Black Hole
Mergers
Raghu Kulkarni
1, ∗
1
Independent Researcher, Calabasas, CA 91302, USA
(Dated: February 16, 2026)
The Hawking Area Theorem asserts that the horizon area of a black hole cannot decrease, a
prediction consistent with current gravitational wave observations to within ∼ 1σ. However,
discrete approaches to quantum gravity such as the Cellular Automaton interpretation or
Crystalline Vacuum models suggest that the continuum approximation of General Relativity
breaks down at the horizon boundary. In the Selection-Stitch Model (SSM), we identify
the horizon as a domain wall subjected to the stress of a “Frustrated Sintering” transition
(K = 12 → 13). By analyzing the energetics of the Face-Centered Cubic (FCC) unit cell
in an Effective Field Theory (EFT) limit, we show that the preservation of bulk Lorentz
invariance forces this stress to split into orthogonal response modes: a “soft” displacement
mode along the normal (into the lattice void) and a “stiff” elastic mode along the tangent.
This derives a universal Area Inflation Factor of ∆A ≈ 7.13%. We demonstrate that this
geometric bias is scale-invariant and independent of merger kinematics, providing a precise,
falsifiable target for Next-Generation (XG) detectors. A case study applying this prediction
to the recent GW250114 event demonstrates that the SSM prediction lies within the 1σ
credible regions of recent independent analyses.
I. INTRODUCTION
Testing the Kerr hypothesis requires precision measurements of the post-merger ringdown spec-
trum. To date, observations have shown consistency with the “No-Hair” theorem of General Rel-
ativity (GR) [3]. The measured remnant area A
f
is generally consistent with the Kerr prediction
derived from the remnant mass and spin.
However, the unification of gravity with quantum mechanics strongly suggests that the contin-
uum approximation of spacetime must break down at the horizon scale. Discrete vacuum models,
such as those proposed by ’t Hooft [1] and Volovik [2], posit that the vacuum possesses a lattice-
like microstructure. In the continuum limit (a → 0), these models recover the Bekenstein-Hawking
entropy scaling (S ∝ A) [4]. Yet, at finite lattice spacing, they predict specific geometric corrections.
In the Selection-Stitch Model (SSM) [5], the vacuum is a discrete tensor network. The extreme
2
curvature at a black hole horizon stresses this lattice, driving it toward a higher-coordination
“sintered” phase (K = 13). Unlike neutron stars, where bulk pressure supports a volumetric phase
change [6], the vacuum horizon is a domain wall that frustrates this transition. This paper derives
the precise geometric signature of this frustration: a systematic inflation of the horizon area that
applies universally to all black hole mergers.
II. PHENOMENOLOGICAL DERIVATION
We model the horizon not as a smooth continuum, but as a crystalline interface undergoing a
“Sintering” phase transition (K = 12 → 13). Since a bulk phase transition would violate Lorentz
invariance (see Sec. III), we propose that the transition is confined to the boundary. We estimate
the area inflation ∆A using three geometric ansatzes based on the FCC lattice structure.
Ansatz 1: Local Faceting. We assume the macroscopic spherical horizon locally aligns with
the principal planes of the vacuum lattice to minimize surface tension (Wulff construction). We
select the (001) plane as the reference surface.
Ansatz 2: The Stress Vector. The topological phase transition requires activating the
octahedral void located at the body center of the unit cell. The stress vector σ driving this
transition connects a lattice node to the void, aligning with the body diagonal (111).
Ansatz 3: Orthogonal Response Decomposition. The stress vector σ projects onto the
surface normal ˆn = (001) with a weight of η = σ · ˆn = 1/
√
3. We decompose the lattice response
into two orthogonal modes:
1. Normal Mode (Filling the Void): The component parallel to ˆn represents purely kine-
matic displacement into the empty void. We model this as a linear density correction:
ξ = 13/12.
2. Tangential Mode (Surface Stretch): The component perpendicular to ˆn represents elas-
tic stretching of the existing surface bonds. We model this using the holographic scaling
A ∼ V
2/3
, yielding a correction of ξ
2/3
.
Combining these contributions yields the Geometric Inflation Factor:
∆A
geo
=
1
√
3
13
12
| {z }
Soft Mode
+
1 −
1
√
3
13
12
2/3
| {z }
Stiff Mode
−1 ≈ 0.0713 (1)
3
This yields a precise, universal prediction for all binary black hole mergers:
A
SSM
= A
GR
(M
f
, χ
f
) × 1.0713 (2)
Independence from Kinematics: Crucially, this factor depends only on the topology of the
unit cell (K = 12) and the stress vector of the transition (⟨1, 1, 1⟩). It is independent of the dynamic
parameters of the merger, such as the mass ratio q, the impact velocity v, or the initial spins χ
1,2
.
While these parameters determine the Baseline GR Area (A
GR
) via the radiated energy E
rad
, the
percentage inflation applied to that baseline is a fixed geometric constant of the vacuum.
III. THEORETICAL CONSTRAINT: THE ANISOTROPY BARRIER
A critical objection to vacuum sintering is the preservation of Lorentz invariance. We explicitly
calculate the stress tensor to show why a bulk phase transition is forbidden, forcing the stress to
pile up at the horizon boundary.
For the standard K = 12 FCC vacuum, the sum of the normalized unit vectors ˆn
i
over the
unit cell yields an isotropic tensor:
S
µν
K=12
=
12
X
i=1
ˆn
µ
i
ˆn
ν
i
= 4δ
µν
(3)
Here ˆn
i
denotes the unit vector along each bond (|ˆn
i
| = 1), in contrast to the integer hopping vectors
used in lattice field theory conventions. This isotropy ensures that the speed of light c ∝
√
S is
invariant in all directions, recovering the continuum Lorentz symmetry.
However, the nucleation of the 13th node at the octahedral void (body center) introduces a
symmetry-breaking term. The normalized unit vector to the void is ˆn
13
=
1
√
3
(1, 1, 1). The tensor
sum for the sintered state becomes:
S
µν
K=13
= S
µν
K=12
+ ˆn
µ
13
ˆn
ν
13
= 4δ
µν
+
1
3
J (4)
where J is the all-ones matrix. The off-diagonal terms (1/3) explicitly break rotation invariance.
Physical Implication: A bulk transition to K = 13 would destroy the isotropy of the vac-
uum, producing a measurable violation of Lorentz invariance. Therefore, the bulk vacuum must
remain in the K = 12 state. The “Soft Mode” derived in Section II represents the boundary de-
formation required to shield the bulk from this symmetry-breaking stress. The horizon inflates to
accommodate the frustrated transition that cannot propagate inward.
4
IV. DISTINGUISHABILITY: SCALE INVARIANCE AS A PHASE TRANSITION
The SSM prediction is distinguishable from other Quantum Gravity (QG) corrections by a
unique feature: Scale Invariance.
Standard perturbative corrections scale as (L
P
/R
H
)
2
, vanishing for astrophysical black holes.
In contrast, the SSM predicts a **constant 7.13% inflation** regardless of mass. We argue this is
the signature of a Vacuum Phase Transition. Just as the density difference between water and
ice (≈ 9%) is an intensive property independent of the ocean’s size, the “sintering” of the vacuum
lattice is a change of state. The 7.13% represents the latent volume expansion of the spacetime
medium itself. This predicts that “geometric bias” should persist even for supermassive black holes,
a claim falsifiable by future LISA observations.
V. APPENDIX A: CONSISTENCY CHECK WITH GW250114
The recent detection of GW250114, the loudest gravitational wave signal to date (SNR ≈ 80),
allows us to check the SSM prediction against current observational constraints. While standard
GR (∆A = 0) remains consistent with the data, the SSM prediction (∆A ≈ +7%) also lies within
the 1σ credible intervals of multiple independent analyses.
1. The Amplitude Boost
Using a parametrized effective-one-body waveform model (pSEOBNR), Grimaldi et al.
(2026) constrained deviations in the peak gravitational wave amplitude at merger [7].
• Measurement: They report a deviation of δA
22
= 0.06
+0.13
−0.11
(Median +6%).
• SSM Prediction: The SSM predicts an area inflation of +7.13%. Since gravitational wave
amplitude scales with the radiating surface area, this predicts a corresponding amplitude
boost of ≈ 7%.
• Comparison: The SSM prediction (+7.13%) falls within the 1σ error bars of the measure-
ment. The data is consistent with both Standard GR (0%) and the SSM (+7%), with the
median value closer to the SSM prediction.
5
2. The Mass Shift
The LVK analysis [3] measured the fractional difference between the remnant mass inferred from
the inspiral versus the ringdown.
• Measurement: ∆M
f
/
¯
M
f
= 0.02
+0.07
−0.06
(a +2% shift).
• SSM Prediction: Since Horizon Area scales as M
2
, a 7.13% area inflation implies a mass
inflation of
√
1.0713 − 1 ≈ 3.5%.
• Comparison: The SSM prediction (+3.5%) is fully consistent with the measurement (+2%),
lying near the center of the posterior distribution.
3. The “Sintering” Anomaly at t = −7M
Standard GR models struggle to explain the energy dynamics immediately preceding the merger
peak.
• Observation: Lu et al. (2025) identified a “prominent peak” in the residual strain at
t ≤ −7M
f
that could not be removed by standard Kerr templates [8].
• SSM Mechanism: The SSM identifies this timestamp as the “Flash Freeze” event—the
moment the vacuum lattice crystallizes under critical pressure, releasing the latent heat that
drives the subsequent horizon inflation.
4. Nonlinearity and Absence of Echoes
• Nonlinearity: Wang et al. (2026) detected six nonlinear quadratic modes in the ringdown
(Bayes Factor = 74), confirming that the merger phase is governed by nonlinear dynamics
consistent with a phase transition [9].
• No Echoes: Wu et al. (2025) found no statistical evidence for late-time echoes [10]. This
confirms that the SSM horizon is dissipative (freezing/absorbing) rather than reflective (like
a wormhole or firewall), distinguishing it from other Exotic Compact Objects.
Conclusion: The GW250114 data exhibits a phenomenology—a pre-merger energy spike (t =
−7M), a median amplitude boost (+6%), and a mass shift (+2%)—that accommodates the precise
6
+7.13% Geometric Horizon Inflation predicted by the Selection-Stitch Model. While not a
definitive confirmation, the alignment suggests the SSM is a viable candidate for physics beyond
the Standard Model.
∗
raghu@idrive.com
[1] G. ’t Hooft, The Cellular Automaton Interpretation of Quantum Mechanics, Springer (2016).
[2] G. E. Volovik, The Universe in a Helium Droplet, Oxford University Press (2003).
[3] A. G. Abac et al. (LVK Collaboration), “Black Hole Spectroscopy and Tests of General Relativity with
GW250114,” Phys. Rev. Lett. 136, 041403 (2026). [arXiv:2509.08099]
[4] J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).
[5] R. Kulkarni, “The Selection-Stitch Model (SSM): Space-Time Emergence via Evolutionary Nucleation,”
Zenodo (2026). [DOI: 10.5281/zenodo.18138227]
[6] R. Kulkarni, “Resolution of the Neutron Star Radius and Mass Anomalies via Geometric Vacuum
Sintering,” Zenodo (2026). [DOI: 10.5281/zenodo.18411594]
[7] L. Grimaldi et al., “Plunge-Merger-Ringdown Tests of General Relativity with GW250114,”
arXiv:2601.13173 (2026). [arXiv:2601.13173]
[8] N. Lu et al., “GW250114 reveals black hole horizon signatures,” arXiv:2510.01001 (2025).
[arXiv:2510.01001]
[9] Y.-F. Wang et al., “A nonlinear voice from GW250114 ringdown,” arXiv:2601.05734 (2026).
[arXiv:2601.05734]
[10] D. Wu et al., “Model-independent search of gravitational wave echoes in LVK data,” arXiv:2512.24730
(2025). [arXiv:2512.24730]
