Two Schwarzschild-type metrics with the NGC 4649 dark matter halo profile are constructed to estimate shadow radii and derive Smarr-type thermodynamic relations, but a factor-of-3 error in the photon sphere equation and a 100-fold error in surface gravity undermine the central results.
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Supermassive black hole in NGC 4649 (M60) with a dark matter halo: Impact on shadow measurements and thermodynamic properties
Two Schwarzschild-type metrics with the NGC 4649 dark matter halo profile are constructed to estimate shadow radii and derive Smarr-type thermodynamic relations, but a factor-of-3 error in the photon sphere equation and a 100-fold error in surface gravity undermine the central results.