New phenomena with the f(R)-theory of gravitation in a central gravitational field

Abstract The f(R)-theory (of gravitation) is an extension of Einstein’s general theory of relativity (GR) but if a spherically symmetric vacuum solution of the Einstein equation in the GR is always stationary, a spherically symmetric vacuum solution of an f(R)-theory is not necessary stationary. This may have interesting consequences. In comparison with the GR, a process such as a planet’s motion (its orbital precession and parameters) and a gravitational deflection of light now get a correction which is a constant for a static central field and varies with time for a non-static central field even from a source of a constant mass, unlike the corresponding GR value not changing in the same situation. In particular, a spherically symmetric source may radiate gravitational waves. This phenomenon cannot happen in the GR. The present work is an extended version based on a presentation in the 44th Vietnam conference on theoretical physics (Dong Hoi, 29 July - 01 August 2019).