A de Sitter region at every black-hole core: discrete causal-set evidence and a canonical regular continuum metric
Abstract
Abstract We close the Schwarzschild central-singularity problem within a nonlocal quadratic-gravity (NQG) model with an entire-function spin-2 form factor and a fakeon prescription at its first positive real zero, instantiating Spectral Causal Theory (SCT, the strict gravitational sector of Causal Architecture Theory) as the specific realisation. The closure is presented at two complementary levels. (I) Fundamental causal-set level. A finite-N causal-set sprinkling of the Schwarzschild interior to within eps_r = 10^-2 M of the classical singularity shows that the maximum local causal-degree scales as N^(1.04 +/- 0.02) and the discrete curvature proxy max/mean saturates at a bounded value ~8.4, independent of eps_r. By contrast the Hayward effective metric saturates the same proxy at ~3.3. At the fundamental discrete level, both spacetimes give an empirically bounded curvature proxy under finite causal-set sprinkling; the classical Schwarzschild singularity does not appear as a power-law divergence in this operational measure. (II) Coarse-grained continuum level. The leading-order effective metric for a vacuum black hole in the model is, by the no-modulus locking, the Hayward functional form with the de Sitter core scale fixed to the model's spin-2 fakeon-pole inverse, ell_dS = 1/m_(2,pole), where m_(2,pole) = Lambda sqrt(z_1) and z_1 = 2.41483889... is the first positive real zero of the canonical transverse-traceless form factor. The resulting black hole carries no free…
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