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

TL;DR

This paper investigates how a kinematic coupling of a scalar field to Einstein tensor influences gravitational collapse, showing black hole formation with horizons and satisfying energy conditions.

Contribution

It introduces the effect of kinematic Einstein tensor coupling on scalar field collapse within Horndeski theory, revealing new dynamics and black hole formation conditions.

Findings

Collapse time depends on derivative coupling value.

A horizon forms protecting the singularity.

Black hole forms with a Schwarzschild-AdS exterior.

Abstract

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.