KeywordsModified gravity,black hole, neutron and boson star
Possible solutions to the mysterious problem of dark matter and dark energy in cosmology consists in adding one or several new fields to the minimal Einstein-Hilbert theory. One class of these extensions constitute the so called Hornedski theory. Although these extended gravity are expected to present significant difference at large scale, small modifications are also expected to occur on the -small scale- basic compact objects of these theories, namely on black holes, boson stars and neutron stars. These modifications can affect several properties: temperature-entropy relation, stability, effect of magnetic and electric charge or rotation. Some of these properties can be studied by means of semi-analytical of numerical methods.