The Modified Schwarzschild Radius with Hubble Field and its Connection to Dark Matter

The classical Schwarzschild radius defines the boundary at which an object becomes a black hole. In an expanding universe governed by the Hubble flow, this concept must be generalized. We derive the modified Schwarzschild radius by including the repulsive Hubble potential into the escape velocity condition v=c. The resulting expression separates the total mass of a system into two distinct terms: one scaling linearly with the radius, M_1∝R, and one scaling with the volume, M_2∝H^2⋅R^3.Applying this decomposition to the Universe itself, we find that the ratio M_2/M_1 =H^2⋅R^2/c^2 ≡ζ is not arbitrary. Using the precise measurements of the Planck mission (Ω_vis/Ω_tot=0,049, Ω_(E_dark )/Ω_tot=0,683, Ω_dark/Ω_tot=0,268), we obtain ζ=5,47±0,1. This value is in excellent agreement with the ratio derived from the modified Schwarzschild radius when the Universe's effective radius is taken as R=c/(H_0⋅ ζ)≈2,2⋅10^26 m.Remarkably, without the Hubble modification, the Universe would lie deep inside the classical black hole region. Instead, it resides exactly on the boundary defined by the modified Schwarzschild radius. This suggests that the observed dark matter abundance may be a direct consequence of the Hubble expansion rather than an exotic particle.We discuss the implications of this result, including whether the Universe's mass is constant or dynamically tracks this boundary, and how this relates to the Rest Angular Momentum (RAM) model. The findings provide a novel, testable link between cosmology and observations.