The leading-soft cubic graviton self-interaction on the black-hole horizon

• URL: http://arxiv.org/abs/2607.21066v1
• Date: Thu, 23 Jul 2026 08:59:13 GMT
• Title: The leading-soft cubic graviton self-interaction on the black-hole horizon
• Abstract summary: We extend the Einstein-Hilbert action to cubic order about the Schwarzschild horizon.<n>We derive the cubic graviton self-interaction on the Gaddam-Groenenboom-'t'Hooft framework.<n>We simulate the real-time dynamics of the resulting Hamiltonian on IBM Qiskit/Aer.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 (GGV) 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, because with the trace/transverse-scalar sector switched off the fluctuation reduces to a two-dimensional block whose $\sqrt{-g}\,R$ is a total (Euler) derivative at every order in $κ$. We prove this by an explicit closed-form reduction and exhibit the cancellation term by term. It is a `framework-specific' statement, even RW gauge, GGV sector, leading soft order, not a gauge-invariant theorem of general relativity. The theorem is exact, but the quantized vertex inherits a $\sim\!20\%$ soft/scheme systematic at the only simulable multiplet ($\ell=2$), which we state explicitly. We then simulate the real-time dynamics of the resulting Hamiltonian on IBM Qiskit/Aer with exact cross-checks. Two structural facts, a conserved charge that only the cubic vertex violates, opening $φφ\to hh\to4φ$, and a provably resonance-free boost spectrum (gap $\to1/2$), already predict that the longitudinal channel is perturbatively rigid; the simulation confirms this quantitatively and measures the residual dressing ($d_{\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar references) rather than discovering it. A symmetry-exact total-occupation truncation yields the first sector-resolved level statistics, indicative of intermediate behaviour on Hilbert spaces too small to be decisive. All circuit results agree with exact diagonalization, every headline number carries a stated systematic, and hardware execution is deferred behind a quantified noise budget.

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