Quantum Pressure as a Fifth Fundamental Force: Evidence from Black Hole Core Physics

We propose that quantum pressure in black hole cores constitutes an effective fifth fundamentalinteraction: a repulsive contribution that becomes dynamically relevant only at ultra-high densityand curvature, preventing singularity formation by counteracting gravitational collapse nearPlanck-scale densities (ρ ≳ 1096 kg/m3). The intent is conservative: we do not alter generalrelativity (GR) in regimes where it has been tested. Instead, we represent the ultravioletcompletion of collapse by an additional effective stress-energy component confined to the deepinterior.Starting from the Heisenberg uncertainty principle and dimensional analysis at the Plancklength, we motivate a characteristic pressure scale PP ∼ ℏc/ℓ4P and implement it phenomenologi-cally through a turn-on function of ρ/ρPlanck. We then quantify how such a compact interiormodification can (or cannot) manifest observationally: (i) ringdown quasi-normal mode (QNM)shifts are generically suppressed by high powers of rc/rs for astrophysical black holes, (ii) horizon-scale imaging and photon-ring shifts are likewise suppressed because they are controlled by thegeometry near the photon sphere, and (iii) extreme mass-ratio inspirals (EMRIs) are emphasizedas a cumulative-phase amplifier in which even tiny conservative corrections could, in principle,become detectable over ∼ 105 cycles. We also clarify what is meant by “fifth force” in thiswork: an effective, ultra-short-range repulsion emergent in the UV regime, not a new long-rangeYukawa interaction subject to laboratory fifth-force constraints. The paper concludes with afalsifiability roadmap: specify interior solutions and matching conditions, compute perturbationboundary conditions and waveform templates, and constrain the onset parameter and functionalform with future gravitational-wave and EMRI data.