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Constraints on Barrow entropy from M87* and S2 star observations

We use data from M87* central black hole shadow, as well as from the S2 star observations, in order to extract constraints on Barrow entropy. The latter is a modified entropy arising from quantum-gravitational effects on the black hole horizon, quantified by the new parameter $Δ$. Such a change in entropy leads to a change in temperature, as well as to the properties of the black hole and its shadow. We investigate the photon sphere and the shadow of a black hole with Barrow entropy, and assuming a simple model for infalling and radiating gas we estimate the corresponding intensity. Furthermore, we use the radius in order to extract the real part of the quasinormal modes, and for completeness we investigate the spherical accretion of matter onto the black hole, focusing on isothermal and polytropic test fluids. We extract the allowed parameter region, and by applying a Monte-Carlo-Markov Chains analysis we find that $ Δ\simeq 0.0036^{+0.0792}_{-0.0145}$. Hence, our results place the upper bound $Δ\lesssim0.0828$ at 1$σ$, a constraint that is less strong than the Big Bang Nucleosynthesis one, but significantly stronger than the late-time cosmological constraints.