ИСТИНА

We consider a general dynamical, spherically symmetric background in Horndeski theory. Within this framework, we analyze the stability conditions for high-energy modes and study the issue of the no-go theorem for cubic and quartic subclasses of Horndeski theory. In particular, we formulate the no-go theorem for weak dependence on one variable (time or radial) and derive its generalization to the cases which could be reduced by coordinate transformation to scenarios where the scalar field has weak dependence on one of the coordinates in the cubic subclass of Horndeski theory. Moreover, we show that a wide class of singular solutions is also prohibited within the outlined subclass of Horndeski theory. Furthermore, we explore the possibility of expanding the no-go theorem to the quartic subclass of Horndeski theory, using the method previously applied to the cubic subclass.