Gravitational Leakage: The Hawking Channel

Established physics. Hawking radiation establishes that the gravitational absorbers we call black holes do not absorb perfectly — c sets a nonzero temperature at the horizon.

1.1 — Setup

Consider a Schwarzschild black hole of mass M. The event horizon is at the Schwarzschild radius:

r_s = 2GM/c² (1.1)

Classical analysis: nothing escapes. Leakage ratio η = 0 (perfect absorption in the classical limit). Hawking (1975) demonstrated that quantum field theory on curved spacetime produces a correction. The black hole emits thermal radiation at temperature:

T_H = ℏc³ / (8πk_B G M) (1.2)

1.2 — Where c appears

The surface gravity of a Schwarzschild black hole is κ = c⁴/(4GM). The Hawking temperature is derived from the surface gravity: T_H = ℏκ/(2πc k_B). c³ appears in the numerator. The temperature is nonzero for any finite M precisely because c is finite and nonzero.

1.3 — Luminosity

Total Hawking luminosity:

L = ℏc⁶ / (15360π G² M²) (1.3)

For a solar-mass black hole: T_H ≈ 6 × 10⁻⁸ K, L ≈ 9 × 10⁻²⁹ W. The net leakage ratio is approximately 10⁻¹⁷ relative to CMB irradiance.

1.4 — Structural features

Claim C1 (Established). Gravitational absorbers exhibit six structural features: (S1) absorption is near-perfect but not perfect, η < 1; (S2) leakage is thermal (Planck spectrum at T_H); (S3) leakage carries boundary information (greybody factors), not input information; (S4) leakage is wavelength-dependent; (S5) spherical geometry enhances absorption; (S6) c is the constraining constant that makes T_H > 0. [Hawking 1975; Bekenstein 1973]