In order to classify and understand the spacetime structure, investigation of the geodesic motion of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in t
he black hole dictionary attracted much attention. In this paper, we give a full description of geodesic motions in three-dimensional spacetime. We investigate the geodesics near charged BTZ black holes and then generalize our prescriptions to the case of massive gravity. We show that electric charge is a critical parameter for categorizing the geodesic motions of both lightlike and timelike particles. In addition, we classify the type of geodesics based on the particle properties and geometry of spacetime.
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.
In this paper, we investigate thermodynamical structure of dyonic black holes in the presence of gravitys rainbow. We confirm that for super magnetized and highly pressurized scenarios, the number of black holes phases is reduced to a single phase. I
n addition, due to specific coupling of rainbow functions, it is possible to track the effects of temporal and spatial parts of our setup on thermodynamical quantities/behaviors including equilibrium point, existence of multiple phases, possible phase transitions and conditions for having a uniform stable structure.
In this paper, we investigate a class of $5$-dimensional black holes in the presence of Gauss-Bonnet gravity with dyonic charges. At first step, thermodynamical quantities of the black holes and their behaviors are explored for different limits. Ther
mal stability and the possibility of the van der Waals like phase transition are addressed and the effects of different parameters on them are investigated. The second part is devoted to simulation of the trajectory of particles around these black holes and investigation of the angular frequency of particles motion. The main goal is understanding the effects of higher curvature gravity (Gauss-Bonnet gravity) and magnetic charge on the structure of black holes and the geodesic paths of particles moving around these black holes.
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.
We consider a model of $F(R)$ gravity in which exponential and power corrections to Einstein-$Lambda$ gravity are included. We show that this model has 4-dimensional Eguchi-Hanson type instanton solutions in Euclidean space. We then seek solutions to
the five dimensional equations for which space-time contains a hypersurface corresponding to the Eguchi-Hanson space. We obtain analytic solutions of the $F(R)$ gravitational field equations, and by assuming certain relationships between the model parameters and integration constants, find several classes of exact solutions. Finally, we investigate the asymptotic behavior of the solutions and compute the second derivative of the $F(R)$ function with respect to the Ricci scalar to confirm Dolgov-Kawasaki stability.
