Static Spherically Symmetric Solution of the Information–Einstein Equations and Black Hole Thermodynamics

Abstract

This paper solves the information–Einstein equations explicitly in a static, spherically symmetric background, obtaining the information-corrected Schwarzschild metric. The core results include: a cooling correction to the Hawking temperature due to information dissipation, T_H = T_H^(0)(1 - λ²/8), where λ ≡ Λ_op Υ_0 r_h² is the dimensionless information dissipation strength; and an information-induced entropy correction, S = A/4 + λ² A/12. Together, these two results reveal a counter-intuitive physical picture: information dissipation does not "heat" a black hole, but rather "freezes" its thermal motion — the stronger the dissipation, the lower the temperature, while the thermodynamic entropy increases because the dissipation channel opens up more microstates. An order-of-magnitude analysis shows that for astrophysical black holes, λ ~ O(1) — the information-dissipation corrections to black hole thermodynamics may not be perturbative, but rather of leading order. As λ approaches the critical value, the surface gravity tends to zero, the Hawking temperature approaches absolute zero, and the black hole enters an "info-geometric death state." This critical mechanism shares the same mathematical structure as the inflationary critical condition (1−c₁)·3H²=0: the information dissipation tensor liberates inflation in cosmology, and terminates black holes in astrophysics. The polarization-dependent attenuation of gravitational waves is also analyzed, yielding Δγ = ε/(κ k⁰). Comparison with EHT observations shows that the shadow radius correction is of order 3λ/4, a linear O(λ) effect, while the temperature correction is O(λ²) — making shadow measurements the most sensitive probe of information dissipation. All correction terms are expressed exclusively in terms of the known parameters of the Order Parameter Spacetime Theory.