4.8 Scale Effects: Small Black Holes Are “Fast,” Large Black Holes Are “Steady”

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The smaller the black hole, the quicker and sharper the behavior near the horizon; the larger the black hole, the slower and smoother the behavior. This contrast is not cosmetic. It follows from how the outer critical boundary, the transition zone, and the core change their timescales, mobility, thickness, and load-sharing as mass scale varies.

I. Response Timescales: Smaller Is Shorter, Larger Is Longer

Near-horizon responses propagate by relay through the “skin” and transition zone within the energy sea. The local tension sets the propagation ceiling, while the distance to cover grows with system size. Therefore, short tracks finish faster in small systems; long tracks run slower in large systems.

• Small black holes: minute–hour rises and decays are common, with closely spaced “steps” in the echo envelope.
• Large black holes: hour–month (even year) variations dominate, echo peaks spread apart, and envelopes flatten.

II. Skin Mobility: Smaller Feels “Light,” Larger Feels “Heavy”

Skin mobility measures how much the outer critical boundary yields under the same stimulus.

1. Why it differs: in smaller systems, a patch on the critical layer holds a smaller “tension budget.” Modest local lifts or geometric rearrangements more easily make the required outward speed dip below the local propagation ceiling, so the boundary moves readily. In larger systems, the same stimulus is diluted over a wider, deeper background, so the boundary resists motion.
2. Manifestations:
   • Small black holes: ephemeral pores light up easily; axial perforation connects more readily; the critical layer behaves like a “thin drumhead.”
   • Large black holes: the layer stays composed; it takes accumulated energy and directional bias to yield—more like a “thick drumhead.”

III. Transition-Zone Thickness: Smaller Is Narrow and Sensitive, Larger Is Thick and Buffering

Viewed as materials, the transition zone works as a piston layer that holds, stores, and releases pressure. As scale grows, geometric size and tension reserves rise, and the zone thickens; as scale shrinks, the buffer thins.

• Thin transition zone (small black holes): storage is limited; stimulation passes through quickly, producing sharp, clustered pulses.
• Thick transition zone (large black holes): inputs are “mashed into paste” first, then released gradually, giving smooth, sustained rises and afterglows.

IV. Load Allocation: The Least-Resistance Path Takes the Share

Outward flux divides among three routes—ephemeral pores, axial perforation, and edgewise band-like subcriticality—according to minimum resistance. Scale reshapes the relative resistance of these routes:

1. Small black holes:
   • Lower perforation threshold: axial bias more easily links pore chains into a line, producing straighter, harder jets.
   • Higher pore density: the skin rewrites easily; pore clusters recur; a soft-leak “base” appears and fades.
   • Weaker edge bands: stripes exist but struggle to align and persist over long distances, so wide reprocessing takes a smaller share.
2. Large black holes:
   • Edge bands dominate: long shear-alignment lengths stabilize band-like subcriticality, strengthening wide-angle outflows and reprocessing.
   • Perforation is choosier: sustained axial channels demand long-lived supply and orientation.
   • Pores are rarer but larger: single pores live longer yet occur less often, tending to be event-driven.

V. One-Page Field Guide: “Fast Small” vs. “Steady Large” in Observations

• Small black holes commonly show: minute–hour fast variability; more frequent hard-spectrum spikes; trains of jet knots moving outward; pronounced, steep common steps across bands; higher near-core polarization that reorders quickly with events.
• Large black holes commonly show: day–month slow undulations; heavy reprocessing and reflection; long-lived ring-edge band brightening; stable blue-shifted absorption and disk-wind signatures; polarization dominated by smooth twists, with band flips co-located with bright sectors but on slower cycles.

These patterns are not exclusive. All three routes often coexist; scale simply biases which one leads.

VI. Summary

Change the mass, and the near-horizon “materials” change with it. Shorter relay paths, lighter skin, and a thinner transition zone make small black holes quick, sharp, and prone to perforation. Longer paths, heavier skin, and a thicker transition zone make large black holes steady, smooth, and edge-favoring. With this picture in mind, the contrast between “jet-loving” and “wind-loving” sources gains a structural explanation.