We consider the effect of a logarithmic f(R) theory, motivated by the form of the one-loop effective action arising from gluons in curved spacetime, on the structure of relativistic stars. In addition to analysing the consistency constraints on the potential of the scalar degree of freedom, we discuss the possibility of observational features arising from a fifth force in the vicinity of the neutron star surface. We find that the model exhibits a chameleon effect that completely suppresses the effect of the modification on scales exceeding a few radii, but close to the surface of the neutron star, the deviation from General Relativity can significantly affect the surface redshift that determines the shift in absorption (or emission) lines. We also use the method of perturbative constraints to solve the modified Tolman-Oppenheimer-Volkov equations for normal and self-bound neutron stars (quark stars).
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