In F(R) gravity, the black hole shadow shift is controlled by a free perturbing function, so matching the M87* and Sgr A* shadow sizes reduces to fitting that function.
For this purpose, we derive the field equation for t he corresponding theory when the general spherically symmetric and static configuration is c onsidered
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Black holes and their shadows in $F(R)$ gravity
In F(R) gravity, the black hole shadow shift is controlled by a free perturbing function, so matching the M87* and Sgr A* shadow sizes reduces to fitting that function.