Observationally Reconstructed Spacetime of NGC 5907: Dark-Matter-Corrected Black Hole Thermodynamics and Galactic Shadow

We present an observationally guided relativistic framework to investigate the thermodynamic and optical properties of a black hole in the NGC 5907 galaxy. By reconstructing the spacetime directly from the observed rotation curve, we obtain a dark-matter-corrected metric that incorporates both the galactic halo and the central compact object. The reconstructed geometry admits horizon solutions, allowing us to evaluate the Hawking temperature, Bekenstein-Hawking entropy, and heat capacity, which indicate a thermodynamically stable supermassive black hole influenced by its dark matter environment. We further analyze photon motion and the resulting gravitational shadow, deriving the photon sphere, critical impact parameter, and shadow size. Comparison with WISE W1 infrared photometry shows consistency with the predicted suppression of photon escape near the shadow radius. These results establish a unified link between galactic rotation curves, dark matter, black hole thermodynamics, and observable photometric signatures.