Gravitational Collapse of a Homogeneous Scalar Field Coupled Kinematically to Einstein Tensor

We study the gravitational collapse of a homogeneous time-dependent scalar field that, besides its coupling to curvature, it is also kinematically coupled to the Einstein tensor. This coupling is a part of the Horndeski theory and we investigate its effect on the collapsing process. We find that the time required for the scalar field to collapse depends on the value of the derivative coupling and the singularity is protected by a horizon. Matching the internal solution with an external Schwarzschild- AdS metric we show that a black hole is formed, while the weak energy condition is satisfied during the collapsing process. The scalar field takes on a finite value at the singularity.