| Summary: | Quark star models with realistic equation of state in nonperturbative f(R) gravity are considered. The mass-radius relation for f(R)=R+αR2 model is obtained. Considering scalar curvature R as an independent function, one can find out, for each value of central density, the unique value of central curvature for which one has solutions with the required asymptotic R→0 for r→∞. In other words, one needs a fine-tuning for R to achieve quark stars in f(R) gravity. We consider also the analogue description in corresponding scalar-tensor gravity. The fine-tuning on R is equivalent to the fine-tuning on the scalar field ϕ in this description. For distant observers, the gravitational mass of the star increases with increasing α (α>0) but the interpretation of this fact depends on frame where we work. Considering directly f(R) gravity, one can say that increasing of mass occurs by the “gravitational sphere” outside the star with some “effective mass”. On the other hand, in conformal scalar-tensor theory, we also have a dilaton sphere (or “disphere”) outside the star but its contribution to gravitational mass for distant observer is negligible. We show that it is possible to discriminate modified theories of gravity from General Relativity due to the gravitational redshift of the thermal spectrum emerging from the surface of the star. Keywords: Modified gravity, Compact stars, Quark stars
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