Calculation of Black Hole Shadow Diameter via Space-Time Duality Principle

Abstract: Introduction of the Huang Metric, which incorporates a quantum gravity correction term in the metric: \frac{2kG_hM^2(\ln r+1)}{c^2 r}. This unified framework calculates both the black hole event horizon and photon sphere, enabling precise prediction of shadow diameter without requiring a spin parameter (spin is typically a post-observation fitting parameter).
Key Formula:
Huang Metric Horizon Equation:
g_{tt} = 0:r_h = \frac{2GM}{c^2} + \frac{2kG_hM^2(\ln r_h +1)}{c^2}

Results and Observational Verification:Black Hole    Theoretical Shadow Diameter (μas)    EHT Observation (μas)    Agreement
Sgr A* (Milky Way)    43.41 – 53.96    51.8 ± 7    Covers error band
M87* (M87 Galaxy)    38.63 – 46.71    42 ± 3    Fully covered Conclusions:
1. Eliminates spin dependence: Shadow diameter is determined solely by mass M and mass ratio k, with no assumption of black hole spin.
2. Observational evidence for quantum gravity: The logarithmic correction term \ln r—directly reflecting quantum topological effects—is confirmed by EHT data.
3. Analytical calculations replace observational fitting: All results are derived through analytical calculations, significantly improving computational efficiency.