Hidden by Exponential Screening: The Invisibility of the Dymnikova Black Hole de Sitter Core to Accretion Observables

Abstract

The Dymnikova spacetime replaces the Schwarzschild singularity with a de Sitter core, and its lapse deviates from Schwarzschild by a factor decaying as $e^{-r^3/(2l_{\rm cr}^2M)}$. Whether this screening renders the core invisible to accretion has remained an open quantitative question. We address it with GRHD simulations of BHL accretion onto Dymnikova BH for six values of the critical length, $0.1M\le l_{\rm cr}\le 1.1M$, the last being 97% of the extremal value. All runs share identical gas parameters and resolution, so any difference in the flow must originate from the geometry. The dynamically relevant quantity is the gravitational acceleration, whose deviation reaches 12% at the inner boundary for the most strongly corrected model, yet the flow responds only locally: the post-shock density drops by 10% in the innermost zone and the quiet-phase accretion rate by 0.12%, with no effect beyond $r\simeq2.7M$. Because runs differing by as little as $\sim 10^{-10}$ in the metric decorrelate completely once the shock-cone instability saturates, we compare models statistically using ensembles of independent realizations. The time-averaged accretion rate is then independent of $l_{\rm cr}$ to within 0.8% $(2σ)$ at all radii; the variability amplitude, shock-cone opening angle $(1.077\pm0.003 rad)$, and stagnation radius $(26.8\pm0.3M)$ vary only within the realization scatter; the propagation lags $(75.5\pm1.0M$ and $31.6\pm0.4M)$ agree to within 1.6%; and no power spectrum carries a detectable core signature. Accretion onto a Dymnikova BH is therefore observationally indistinguishable from accretion onto a Schwarzschild black hole: timing observations test the shock-cone mechanism, not the regular core. More broadly, ensemble-based statistical comparisons are essential before differences between simulated accretion flows in different spacetimes can be interpreted as physical.