Spacetime Duality Principle: Calculations of Black Hole Temperature and Radiation

Abstract: 1. A Novel Physical Mechanism for Black Hole Temperature
(Based on Matter Creation via Quantum Gravity in Black Hole Interiors)
Temperature Formula:
T = \left( \frac{c^7 \eta U_{QG}}{32\pi G^3 M_{BH}^3 \sigma} \right)^{1/4}
Key Parameters:
• U_{QG}: Extreme repulsive quantum gravitational potential energy within the black hole, calculated by integrating over the matter creation zone (\ell < r < r_{CFT}).
• \eta: Quantum spacetime curvature efficiency factor, dependent on the baryonic mass ratio of galaxies (\eta \propto (M_{\text{gal}}/M_{\text{MW}})^2).

2. Three-Stage Evolution of Radiation Energy
(1) Internal Generation:
• Planck Photon Energy: E_{\text{Planck}} = 2.821 k_B T (Sgr A*: 2.247 GeV).
(2) Horizon Tunneling:
• Redshift Attenuation: Photon energy reduces to E_{\text{photon}} \in [E_{\text{Planck}} \sqrt{A(r_h)}, E_{\text{Planck}} \sqrt{A(r_{ph})}] (Sgr A* lower limit: 4.55 \times 10^{-17} eV).
• Redshift Factor: \sqrt{A(r)} \approx \sqrt{\Lambda_{\text{cosmo}} / \Lambda(r)}.
(3) Gravitational Wave Standing Wave Coupling:
• Energy Addition: E_{GW}(r_{sh}) = \frac{c^2 \eta}{24G} \frac{(A_{\mu\nu}^0)^2}{|q(r_h)^2|} (r_{sh}^3 - r_h^3) (Sgr A* upper limit: 9.85 GeV).
• Final Energy Range: E \in [10^{-17} \text{ eV}, 10.8 \text{ GeV}] (covers Fermi-LAT observations at 0.1–10 GeV).
 Observational Verification:
Target    Theoretical Prediction    Observed Data    Instrument
Sgr A* Flare Period    89.8–111.6 seconds    90–120 seconds (JWST)    NIRCam/JWST
M87* Flare Period    43–52 hours    24–48 hours (H.E.S.S.)    H.E.S.S.
Sgr A* Spectrum    0.1–10 GeV non-thermal    Matched (Fermi-LAT)    Fermi-LAT

3. Conclusion：
The Spacetime Duality Principle bridges the quantitative gap between black hole temperature, quantum gravitational potential, and observable radiation through:
(1) Temperature Formula: Reveals quantum processes in black hole interiors dominate thermodynamics.
(2) Three-Stage Radiation: Unifies explanations for energy spectra, time scales, and polarization.
(3) Six Observational Validations: Includes EHT shadows, Fermi spectra, and JWST flares; predictions for polarization and spectral cutoffs await CTA verification.