The leading-soft cubic graviton self-interaction on the black-hole horizon
Abstract
We expand the Einstein--Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge--Wheeler gauge of the Gaddam--Groenenboom--'t~Hooft near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a vanishing theorem: at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero. This is a framework-specific statement: even RW gauge, GGV sector, leading soft order. The surviving interaction lives in the trace sector; its on-shell equal-ℓ weight W(λ,λ,λ)=−3λ(2λ2+λ+3)/(λ+1)2, follows from two independent derivations agreeing to machine precision. We simulate the resulting Hamiltonian at two complementary scales. On IBM Qiskit/Aer, with exact cross-checks, the hardware-format circuits confirm quantitatively what two structural facts already predict, a conserved charge that only the cubic vertex violates (opening ϕϕ→ hh→4ϕ) and a resonance-free boost spectrum (gap →1/2): the longitudinal channel is perturbatively rigid, and the simulation measures the residual dressing (deff=1.06; multiplicity far from thermal, Poisson, and Haar). A symmetry-graded matrix-product-state evolution then climbs the multipole ladder to sixty modes, the $120$-qubit register, and settles the one question the multiplet cannot: on a late-time measure common to both engines the inelasticity converges to η̅∞≃0.16 (understated by the single multiplet), the dressing stays area-law with peak entanglement ≃0.45 nats far below the Page value, and the result is cutoff-converged and robust to $96$ qubits at larger occupation. The rigidity therefore persists rather than scrambling as the register grows.
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BibTeX
@misc{dutta2026leadingsoft,
title = {{The leading-soft cubic graviton self-interaction on the black-hole horizon}},
author = {Ayanendu Dutta},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.21066},
eprint = {2607.21066},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21066},
}
RIS
TY - UNPB
TI - The leading-soft cubic graviton self-interaction on the black-hole horizon
AU - Ayanendu Dutta
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2607.21066
UR - https://arxiv.org/abs/2607.21066
AB - We expand the Einstein--Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge--Wheeler gauge of the Gaddam--Groenenboom--'t~Hooft near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a vanishing theorem: at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero. This is a framework-specific statement: even RW gauge, GGV sector, leading soft order. The surviving interaction lives in the trace sector; its on-shell equal-ℓ weight W(λ,λ,λ)=−3λ(2λ^2+λ+3)/(λ+1)^2, follows from two independent derivations agreeing to machine precision. We simulate the resulting Hamiltonian at two complementary scales. On IBM Qiskit/Aer, with exact cross-checks, the hardware-format circuits confirm quantitatively what two structural facts already predict, a conserved charge that only the cubic vertex violates (opening ϕϕ→ hh→4ϕ) and a resonance-free boost spectrum (gap →1/2): the longitudinal channel is perturbatively rigid, and the simulation measures the residual dressing (d_eff=1.06; multiplicity far from thermal, Poisson, and Haar). A symmetry-graded matrix-product-state evolution then climbs the multipole ladder to sixty modes, the $120$-qubit register, and settles the one question the multiplet cannot: on a late-time measure common to both engines the inelasticity converges to η̅_∞≃0.16 (understated by the single multiplet), the dressing stays area-law with peak entanglement ≃0.45 nats far below the Page value, and the result is cutoff-converged and robust to $96$ qubits at larger occupation. The rigidity therefore persists rather than scrambling as the register grows.
ER -