Orbiting naked singularities in large- $\omega $ Brans–Dicke gravity
Résumé
Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the $\omega \longrightarrow \infty $ limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.