Using the latest most accurate values of post-Newtonian parameters γ and β obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar–tensor representation. We show that the presence of a light scalar field in this theory does not contradict the experimental data based not only on the γ parameter (as was shown earlier), but also on all other PPN parameters. The application of parameterized post-Newtonian formalism to gravitational theories with massive fields is also discussed.

Gauss-Bonnet gravity provides one of the most promising frameworks for studying curvature corrections to the Einstein action in supersymmetric string theories while avoiding ghosts and keeping second-order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for a long time, the Kerr-Gauss-Bonnet metric was missing. A five dimensional Gauss-Bonnet solution is obtained analytically for spinning black holes, and the related thermodynamical properties are briefly outlined.

We discuss a Brans-Dicke model with a cosmological constant, a negative value of the $w$ parameter, and an arbitrary (in general nonvanishing) scale factor at the big bang. The Friedmann equations for a flat universe are considered. The current observational values for Hubble constant $H_0$ and deceleration parameter $q_0$ play the role of initial conditions. We follow the approach of Uehara and Kim in order to solve field equations analytically. In K. Uehara and C. W. Kim [ Phys. Rev. D 26, 2575 (1982)] only positive values of $w$ were considered; we extend the study to a complete set of possible $w$ values. Our main result is that the scale factor (during its evolution back in time direction) may not vanish, unlike in the standard $\Lambda \mathrm{CDM}$ case. In other words, the considered model demonstrates a cosmological bounce instead of the initial singularity. The famous formula (24), that leads to the bounce, is valid only for the dust-filled universe with $p=0$ and, therefore, is not adequate for the early universe hot stage when the bounce happens. So, our results are qualitative in nature and must be used to obtain initial values for the hot stage of the Universe.

We have investigated the equations of geodesics for the black hole solution suggested in [1] in the Randall-Sundrum model with one brane. Being a generalization of the Schwarzschild metric, this solution has a structure like the Reissner-Nordström one, with the “tidal charge” replacing the electric charge. Following our investigation of the behavior of geodesics, we have shown that this solution is consistent with observational data, without predicting the appearance of any fundamentally new effects. A more accurate constraint on the tidal charge is obtained by analyzing circular orbits.

A simple phenomenological extension of the black hole solution with tidal charge is proposed. Empirical data on the Sgr A* black hole is consistent with the suggested metric which serves as a...

The energy flux emitted during the accretion of matter onto a wormhole in the Brans-Dicke theory has been calculated. This characteristic is compared with its values calculated previously for wormholes in general relativity and for a Schwarzschild black hole.