In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass
of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$ and $c_{2}$ are acceptable.
Motivated by importance of the existence of quark matter on structure of neutron star. For this purpose, we use a suitable equation of state (EoS) which include three different parts: i) a layer of hadronic matter, ii) a mixed phase of quarks and had
rons, and, iii) a strange quark matter in the core. For this system, in order to do more investigation of the EoS, we evaluate energy, Le Chateliers principle and stability conditions. Our results show that the EoS satisfies these conditions. Considering this EoS, we study the effect of quark matter on the structure of neutron stars such as maximum mass and the corresponding radius, average density, compactness, Kretschmann scalar, Schwarzschild radius, gravitational redshift and dynamical stability. Also, considering the mentioned EoS in this paper, we find that the maximum mass of hybrid stars is a little smaller than that of the corresponding pure neutron star. Indeed the maximum mass of hybrid stars can be quite close to the pure neutron stars. Our calculations about the dynamical stability show that these stars are stable against the radial adiabatic infinitesimal perturbations. In addition, our analyze indicates that neutron stars are under a contraction due to the existence of quark core.
Inspired by applications of gravitys rainbow in UV completion of general relativity, we investigate charged topological black holes in gravitys rainbow and show that depending on the values of different parameters, these solutions may encounter with
black hole solutions with two horizons, extreme black hole (one horizon) or naked singularity (without horizon). First, we obtain black hole solutions, calculate thermodynamical quantities of the system and check the first law of thermodynamics. Then, we study the thermodynamical behavior of the system including thermal stability and phase transitions. In addition, we employ geometrical thermodynamics to probe phase transition points and limits on having physical solutions. Finally, we obtain heat engines corresponding to these black holes. The goal is to see how black holes parameters such as topological factor and rainbow functions would affect efficiency of the heat engines.
Motivated by recent progresses in the field of massive gravity, the paper at hand investigates the thermodynamical structure of black holes with three specific generalizations: i) Gauss-Bonnet gravity which is motivated from string theory ii) PMI non
linear electromagnetic field which is motivated from perspective of the QED correction iii) massive gravity which is motivated by obtaining the modification of standard general relativity. The exact solutions of this setup are extracted which are interpreted as black holes. In addition, thermodynamical quantities of the solutions are calculated and their critical behavior are studied. It will be shown that although massive and Gauss-Bonnet gravities are both generalizations in gravitational sector, they show opposing effects regarding the critical behavior of the black holes. Furthermore, a periodic effect on number of the phase transition is reported for variation of the nonlinearity parameter and it will be shown that for super charged black holes, system is restricted in a manner that prevents it to reach the critical point and acquires phase transition. In addition, the effects of geometrical structure on thermodynamical phase transition will be highlighted.
Regarding the strong magnetic field of neutron stars and high energy regime scenario which is based on high curvature region near the compact objects, one is motivated to study magnetic neutron stars in an energy dependent spacetime. In this paper, w
e show that such strong magnetic field and energy dependency of spacetime have considerable effects on the properties of neutron stars. We examine the variations of maximum mass and related radius, Schwarzschild radius, average density, gravitational redshift, Kretschmann scalar and Buchdahl theorem due to magnetic field and also energy dependency of metric. First, it will be shown that the maximum mass and radius of neutron stars are increasing function of magnetic field while average density, redshift, the strength of gravity and Kretschmann scalar are decreasing functions of it. These results are due to a repulsive-like force behavior for the magnetic field. Next, the effects of the gravitys rainbow will be studied and it will be shown that by increasing the rainbow function, the neutron stars could enjoy an expansion in their structures. Then, we obtain a new relation for the upper mass limit of a static spherical neutron star with uniform density in gravitys rainbow (Buchdahl limit) in which such upper limit is modified as $M_{eff}<frac{4c^{2}R}{9G}$. In addition, stability and energy conditions for the equation of state of neutron star matter are also investigated and a comparison with empirical results is done. It is notable that the numerical study in this paper is conducted by using the lowest order constrained variational (LOCV) approach in the presence of magnetic field employing AV18 potential.
The paper at hand studies the heat engine provided by black holes in the presence of massive gravity. The main motivation is to investigate the effects of massive gravity on different properties of the heat engine. It will be shown that massive gravi
ty parameters and gravitons mass modify the efficiency of engine on a significant level. Furthermore, it will be shown that it is possible to have the heat engine for non-spherical black holes in massive gravity and we study the effects of topological factor on properties of the heat engine. Surprisingly, it will be shown that the highest efficiency for the heat engine belongs to black holes with hyperbolic horizon, while the lowest one belongs to spherical black holes.
