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.
With the first solution (16) F(r) =γ a2 +r 2 V 2 c − 2M r .(24) we have considerable difficulty in obtaining an analyti- cal solution
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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.