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A deep exploration of the parameter space that relates the interacting equation of state with the bag constant B, and the interaction parameter a, is fundamental for the construction of diverse models of quark stars. In particular, the anisotropy of quark stars with a well-motivated quantum chromodynamics (QCD) equation of state is presented here. The contribution of the fourth order corrections parameter ($\mathrm{a}$) of the QCD perturbation on the radial and tangential pressure generate significant effects on the mass-radius relation and the stability of the quark star. An adequate set of solutions for several values of the bag factor and the interaction parameter are used in order to calculate the relation between the mass, radius, density, compactness, and consequently the maximum masses and the stability. Therefore, while the more interactive quark solution leads to higher masses, the weak interaction among quarks give solutions similar to the widely known MIT bag model., Comment: All comments and suggestions are welcome

The innermost stable circular orbits (ISCOs) around rapidly rotating neutron stars are studied in dilatonic Einstein-Gauss-Bonnet theory. Universal relations for properly scaled ISCO properties are extended from General Relativity to dilatonic Einstein-Gauss-Bonnet theory and additional relations are obtained., Comment: 14 pages, 11 figues

We address quasinormal modes of compact objects in several alternative theories of gravity. In particular, we focus on black holes and neutron stars with scalar hair. We consider black holes in dilaton-Einstein-Gau\ss -Bonnet theory, and in a generalized scalar-Einstein-Gau\ss -Bonnet theory. In the latter case scalarized black holes arise, and we study the stability of the different branches of solutions. In particular, we discuss how the spectrum of quasinormal modes is changed by the presence of a non-trivial scalar field outside the black hole horizon. We discuss the existence of an (effective) minimum mass in these models, and how the spectrum of modes becomes richer as compared to general relativity, when a scalar field is present. Subsequently we discuss the effect of scalar hair for realistic neutron star models. Here we consider $R^2$ gravity, scalar-tensor theory, a particular subsector of Horndeski theory with a non-minimal derivative coupling, and again dilatonic-Einstein-Gau\ss -Bonnet theory. Because of the current lack of knowledge on the internal composition of the neutron stars, we focus on universal relations for the quasinormal modes, that are largely independent of the equations of state and thus the matter content of the stars., Comment: 38 pages, 14 figures

Generalizations of the Schwarzschild and Kerr black holes are discussed in an astrophysically viable generalized theory of gravity, which includes higher curvature corrections in the form of the Gauss-Bonnet term, coupled to a dilaton. The angular momentum of these black holes can slightly exceed the Kerr bound. The location and the orbital frequency of particles in their innermost stable circular orbits can deviate significantly from the respective Kerr values. Study of the quasinormal modes of the static black holes gives strong evidence that they are mode stable against polar and axial perturbations. Future gravitational wave observations should improve the current bound on the Gauss-Bonnet coupling constant, based on observations of the low-mass x-ray binary A 0620-00., Comment: 8 pages, 7 figures

We construct sequences of rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear matter. We analyze the dependence of the physical properties of these neutron stars on the Gauss-Bonnet coupling strength. For a given equation of state we determine the physically relevant domain of rapidly rotating neutron stars, which is delimited by the set of neutron stars rotating at the Kepler limit, the set of neutron stars along the secular instability line, and the set of static neutron stars. As compared to Einstein gravity, the presence of the Gauss-Bonnet term decreases this domain, leading to lower values for the maximum mass as well as to smaller central densities. The quadrupole moment is decreased by the Gauss-Bonnet term for rapidly rotating neutron stars, while it is increased for slowly rotating neutron stars. The universal relation between the quadrupole moment and the moment of inertia found in General Relativity appears to extend to dilatonic Einstein-Gauss-Bonnet theory with very little dependence on the coupling strength of the Gauss-Bonnet term. The neutron stars carry a small dilaton charge., Comment: 24 pages, 15 figures

We present an investigation of spinning black holes in Einstein--Gauss-Bonnet--dilaton (EGBd) theory. The solutions are found within a non-perturbative approach, by directly solving the field equations. These stationary axially symmetric black holes are asymptotically flat. They possess a non-trivial scalar field outside their regular event horizon. We present an overview of the parameter space of the solutions together with a study of their basic properties. We point out that the EGBd black holes can exhibit some physical differences when compared to the Kerr solution. For example, their mass is always bounded from below, while their angular momentum can exceed the Kerr bound, Also, in contrast to the Kerr case, the extremal solutions are singular, with the scalar field diverging on the horizon., Comment: 24 pages, 14 figures

We investigate axial quasi-normal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider 8 realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling., Comment: 15 pages, 9 figures

We consider rapidly rotating black holes and neutron stars in dilatonic Einstein-Gauss-Bonnet (EGBd) theory and determine their quadrupole moments, which receive a contribution from the dilaton. The quadrupole moment of EGBd black holes can be considerably larger than the Kerr value. For neutron stars, the universality property of the $\hat I$-$\hat Q$ relation between the scaled moment of inertia and the scaled quadrupole moment appears to extend to EGBd theory., Comment: 5 pages, 4 figures

The thermodynamics of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole from string theory is reformulated within the context of the recently developed formalism of geometrothermodynamics. The geometry of the space of equilibrium states is curved, but we show that the thermodynamic curvature does not diverge when the black hole solution becomes a naked singularity. This provides a counterexample to the conventional notion that a thermodynamical curvature divergence signals the occurrence of a phase transition., Comment: 10 pages