Relativistic Stars in Beyond Horndeski Theories

This work studies relativistic stars in beyond Horndeski scalar–tensor theories that exhibit a breaking of the Vainshtein mechanism inside matter, focusing on a model based on the quartic beyond Horndeski Lagrangian. We self-consistently derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space–time and show that the Vainshtein breaking branch of the solutions is the physical branch thereby resolving several ambiguities with non-relativistic frameworks. The geometry outside the star is shown to be exactly Schwarzschild-de Sitter and therefore the parameterised post-Newtonian parameter ${\beta }_{{\rm{PPN}}}=1$, confirming that the external screening works at the post-Newtonian level. The Tolman–Oppenheimer–Volkoff (TOV) equations are derived and a new lower bound on the Vainshtein breaking parameter ${{\rm{\Upsilon }}}_{1}\gt -4/9$ is found by requiring the existence of static spherically symmetric stars. Focusing on the unconstrained case where ${{\rm{\Upsilon }}}_{1}\lt 0$, we numerically solve the TOV equations for polytropic and realistic equations of state and find stars with larger radii at fixed mass. Furthermore, the maximum mass can increase dramatically and stars with masses in excess of $3{M}_{\odot }$ can be found for relatively small values of the Vainshtein breaking parameter. We re-examine white dwarf stars and show that post-Newtonian corrections are important in beyond Horndeski theories and therefore the bounds coming from previous analyses should be revisited.