In this work wormholes in viable f (R) gravity models are analyzed. We are interested in exact solutions for stress-energy tensor components depending on different shape and redshift functions. Several solutions of gravitational equations for different f (R) models are examined. The solutions found imply no need for exotic material, while this need is implied in the standard general theory of relativity. A simple expression for weak energy condition (WEC) violation near the throat is derived and analyzed. High curvature regime is also discussed, as well as the question of the highest possible values of the Ricci scalar for which the WEC is not violated near the throat, and corresponding functions are calculated for several models. The approach here differs from the one that has been common since no additional assumptions to simplify the equations have been made, and the functions in f (R) models are not considered to be arbitrary functions, but rather a feature of the theory that has to be evaluated on the basis of consistency with observations for the Solar System and cosmological evolution. Therefore in this work we show that the existence of wormholes without exotic matter is not only possible in simple arbitrary f (R) models, but also in models that are in accordance with empirical data.

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyse the cosmological evolution of wormhole solutions in modified f (R) gravity. We construct a dynamical wormhole that asymptotically approaches FLRW universe, with supporting material going to the perfect isotropic fluid described by the equation of state for radiation and matter dominated universe respectively. Our analysis is based on an approximation of a small wormhole -a wormhole that can be treated as matched with the FLRW metric at some radial coordinate much smaller than the Hubble radius, so that cosmological boundary conditions are satisfied. With a special interest in viable wormhole solutions, we refer to the results of reconstruction procedure and use f (R) functions which lead to the experimentally confirmed ΛCDM expansion history of the universe. Solutions we find imply no need for exotic matter near the throat of considered wormholes, while in the limit of f (R) = R this need is always present during radiation and matter dominated epoch.

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It is a well known result that the effect of vacuum polarization in gravitational fields will lead to a non-minimal coupling between gravity and electromagnetism. We investigate this phenomenon further by considering the description of static magnetic field around a Schwarzschild black hole. It is found that close to the Schwarzschild horizon the magnetic fields can be strongly modified with respect to both cases of magnetic fields on flat spacetime and magnetic fields minimally coupled on curved spacetime. Under the proper sign of the non-minimal coupling parameter, q, the effective fields can undergo large amplifications. Furthermore, we discuss the physical meaning of the singularities that arise in the considered problem. We conclude by discussing the potential observational effects of vacuum polarization on the magnetic fields. In the case of astrophysical black holes, depending on the value of the coupling parameter, significant modifications of the magnetic near the black hole horizons are possible -which could be used to detect the vacuum polarization effect or at least to put constraints on the values of the coupling parameter. Moreover, we show how the considered effect directly constraints the viability of primordial black holes of sizes smaller than that of the Compton wavelength for the electron, and also impacts the distribution of magnetic fields in the early Universe. arXiv:1809.06054v2 [gr-qc]

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole (SBH) on the motion of charged particles are investigated in this work. Using the weak electromagnetic field approximation, we discuss the non-minimal coupling between magnetic fields and gravity caused by the vacuum polarization and study the equations of motion for the case of a magnetic field configuration which asymptotically approaches a dipole magnetic field. It is shown that the presence of non-minimal coupling can significantly influence the motion of charged particles around Black Holes. In particular, the vacuum polarization effect, leading to strong amplification or suppression of the magnetic field strength around the event horizon (depending on the sign of the coupling parameter), can affect the scattering angle and minimal distance for the electrons moving in the gravitational field of the Black Hole as well as the dependence of these parameters on the asymptotic magnetic field strength, initial distance and the Black Hole mass. It is further demonstrated that the non-minimal coupling between gravity and astrophysical magnetic fields, caused by the vacuum polarization, can cause significant changes of the parameter space corresponding to bound trajectories around the Black Hole. In certain cases, the bounded or unbounded character of a trajectory is determined solely by the presence of non-minimal coupling and its strength. These effects could in principle be used as observational signatures of the vacuum polarization effect and also to constrain the value of the coupling parameter.

In this work we investigate the consequences of running gravitational coupling on the properties of rotating black holes. Apart from the changes induced in the spacetime structure of such black holes, we also study the implications to Penrose process and geodetic precession. We are motivated by the functional form of gravitational coupling previously investigated in the context of infra-red limit of asymptotic safe gravity theory. In this approach, the involvement of a new parameterξ in this solution makes it different from Schwarzschild black hole. The Killing horizon, event horizon and singularity of the computed metric is then discussed. It is noticed that the ergosphere is increased as ξ increases. Considering the black hole solution in equatorial plane, the geodesics of particles, both null and time like cases, are explored. The effective potential is computed and graphically analyzed for different values of parameterξ . The energy extraction from black hole is investigated via Penrose process. For the same values of spin parameter, the numerical results suggest that the efficiency of Penrose process is greater in quantum corrected gravity than in Kerr Black Hole. At the end, a brief discussion on Lense-Thirring frequency is also done.

In this work we propose a new general model of eternal cyclic Universe. We start from the assumption that quantum gravity corrections can be effectively accounted by the addition of higher order curvature terms in the Lagrangian density for gravity. It is also taken into account that coefficients associated with these curvature corrections will in general be dependent on a curvature regime. We therewith assume no new ingredients, such as extra dimensions, new scalar fields, phantom energy or special space-time geometries. Evolution of the Universe in this framework is studied and general properties of each phase of the cycle -cosmological bounce, low curvature (ΛCDM) phase, destruction of bounded systems and contracting phase -are analysed in detail. Focusing on some simple special cases, we obtain analytical and numerical solutions for the each phase confirming our analysis.

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