Scalar field as a time variable during gravitational evolution

TL;DR

This paper investigates whether a scalar field can reliably serve as a time variable during the dynamical evolution of gravitational systems, especially near singularities, by analyzing a scalar field collapse in general relativity.

Contribution

It explicitly demonstrates that the scalar field can act as a time parameter in high-curvature regions during gravitational collapse.

Findings

Hypersurfaces of constant scalar field are spacelike near singularities.

Scalar field values change monotonically in regions with spacelike hypersurfaces.

Supports the use of scalar fields as intrinsic clocks in quantum gravity contexts.

Abstract

Using a scalar field as an intrinsic 'clock' while investigating the dynamics of gravitational systems has been successfully pursued in various researches on the border between classical and quantum gravity. The objective of our research was to check explicitly whether the scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity. For this purpose, we analyzed a gravitational collapse of a self-interacting scalar field within the framework of general relativity. The obtained results indicated that the hypersurfaces of constant scalar field are spacelike in dynamical regions nearby the singularities formed during the investigated process. The scalar field values change monotonically in the areas, in which the constancy hypersurfaces are spacelike.