B. Danilă, T. Harko, **F. S. N. Lobo**, M. K. Mak

**Abstract**

We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein condensate stars in the recently proposed hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini *f*(*ℜ*) formalisms. It turns out that the theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. In this paper, we derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework of the scalar-tensor representation of the hybrid metric-Palatini theory, and we investigate their solutions numerically for different equations of state of neutron and quark matter, by adopting for the scalar field potential a Higgs-type form. It turns out that the scalar-tensor definition of the potential can be represented as an Clairaut differential equation, and provides an explicit form for *f*(*ℜ*) given by *f*(*ℜ*)∼*ℜ*+Λ_{eff}, where Λ_{eff} is an effective cosmological constant. Furthermore, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly constructed in both general relativity and hybrid metric-Palatini gravity, thus allowing an in-depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, hybrid gravity stars are more massive than their general relativistic counterparts. Furthermore, two classes of stellar models corresponding to two particular choices of the functional form of the scalar field (constant value, and logarithmic form, respectively) are also investigated. Interestingly enough, in the case of a constant scalar field the equation of state of the matter takes the form of the bag model equation of state describing quark matter. As a possible astrophysical application of the obtained results, we suggest that stellar mass black holes, with masses in the range of 3.8 and 6 *M _{⊙}*, respectively, could be in fact hybrid metric-Palatini gravity neutron or quark stars.

**Keywords**

HIGH-REDSHIFT SUPERNOVAE; HUBBLE-SPACE-TELESCOPE; F R THEORIES; MODIFIED GRAVITY; NEUTRON-STAR; COSMOLOGICAL THEORY; F(R) THEORIES; DARK ENERGY; QUARK STARS; CONSTRAINTS

**Physical Review D**

Volume 95, Issue 4, Page 20

2017 February