UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2026-06-11 23:58
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Conference: Bucharest University Faculty of Physics 2026 Meeting


Section: Theoretical and Computational Physics, Applied Mathematics


Title:
Retarded Self-Energies and Curvature Matching in a Graviton Bound-State Model of Black Holes


Authors:
George CRISTACHE (1), Virgil BĂRAN (1)


*
Affiliation:
1) Faculty of Physics, University of Bucharest, Atomiștilor 405, RO-077125, Măgurele, România


E-mail
george.cristache@s.unibuc.ro


Keywords:
Effective field theory; graviton bound states; Schwarzschild black holes; retarded self-energy; composite operators; coarse-graining; curvature matching


Abstract:
We develop a minimal semiclassical effective-field-theory description of a Schwarzschild black hole modeled as a near-pole graviton bound state. The black-hole sector is represented by an auxiliary collective field J, coupled to a short-scale radiative/probe graviton current and to a deep-infrared constituent mode. Within a projected EMRI regime, the effective Lagrangian separates radiative, deep-IR, and bound-state degrees of freedom, while the near-pole transition band is treated through soft-tie constraints relating the microscopic composite sector to the effective J-field. We show that the retarded self-energy induced by the localized probe factorizes, at leading order, into a short-distance kernel and a slowly varying deep-IR background coefficient. After coarse-graining on the Schwarzschild scale, this produces a local mass-shift term ∆μ 2 R(X)J(X), with nonlocal corrections suppressed by the probe-to-black-hole scale ratio and with the divergent zeroth moment absorbed into EFT counterterms. The resulting renormalized mass shift is then used as the source structure entering a matrix-element matching procedure: rather than inverting distribution-valued propagators, we contract the near-shell equation with an external graviton insertion, control contact terms and off-shell remainders, and project onto the on-shell tensor structure. In this restricted sense, the projected bound-state response is matched to the trace-reversed curvature source of the classical Schwarzschild saddle. The construction is not a first-principles derivation of the Einstein equations, but a coarse-grained EFT matching prescription linking a graviton-bound-state sector to the curvature response used in gravitational-wave calculations.