Shadow of a Charged Rotating Black Hole in f(R)f(R) Gravity

We study the shadow of a charged rotating black hole in $f(R)$ gravity. This black hole is characterized by mass, $M$, spin, $a$, electric charge, $Q$ and $R_{0}$ which is proportional to cosmological constant. We analyze the image of the black hole's shadow in four types 1) at $r\rightarrow\infty$, 2) at $r\rightarrow r_{o}$, in vacuum, 3) at $r\rightarrow\infty$, 4) at $r\rightarrow r_{o}$, for an observer at the presence of plasma. Moreover, we investigate the effect of spin, charge and modfication of gravity on the shape of shadow. In addition, we use two observables, the radius $R_{s}$ and the distortion parameter $\delta_{s}$, characterizing the apparent shape. We show that for all cases, the shadow becomes smaller with increasing electric charge. Also, by increasing the rotation parameters, circular symmetry of the image of black hole's shadow will change. Furthermore, in the presence of plasma, plasma parameter also effects on size of the shadow.Comment: 28 pages,6 tables,43 figure

Thermodynamic geometry of black holes in f(R) gravity

In this paper, we consider three types (static, static charged and rotating charged) of black holes in f(R) gravity. We study the thermodynamical behavior, stability conditions and phase transition of these black holes. It will be shown that, the number and type of phase transition points are related to different parameters, which shows the dependency of stability conditions to these parameters. Also, we extended our study to different thermodynamic geometry methods (Ruppeiner, Weinhold and GTD). Next, we investigate the compatibility of curvature scalar of geothermodynamic methods with phase transition points of the above balck holes. In addition, we point out the effect of different values of spacetime parameters on stability conditions of mentioned black holes.Comment: 45 figures,35 page

f(R) Gravity: From the Pioneer Anomaly to the Cosmic Acceleration

We use metric formalism in $f(R)$ modified gravity to study the dynamics of various systems from the solar system to the cosmological scale. we assume an ansatz for the derivative of action as a function of distance and describe the Pioneer anomaly and the flat rotation curve of the spiral galaxies. Having the asymptotic behavior of action, we propose the action of $f(R) = (R + \Lambda)(1 + \ln(R/R_c)/(R/R_0 + 2/\alpha))$ where in galactic and solar system scales it can recover our desired form. The vacuum solution of this action also results in a positive late time acceleration for the universe. We fix the parameters of this model, comparing with the Pioneer anomaly, rotation curve of spiral galaxies and Supernova Type Ia gold sample data.Comment: 6 pages, 2 figure

Consistency Condition of Spherically Symmetric Solutions in f(R)f(R) Gravity

In this work we study the spherical symmetric solutions of $f(R)$ gravity in the metric formalism. We show that for a generic $f(R)$ gravity, the spherical symmetric solution is consistent with the modified gravity equations except in the case of imposing an extra condition for the metric.Comment: 4 pages, accepted in MPL