Orthogonal Splitting in Degenerate Higher-order Scalar-tensor Theories

TL;DR

This paper analyzes the gravitational field equations in degenerate higher-order scalar-tensor theories, focusing on their degrees of freedom, structure scalars, and realistic models for celestial objects.

Contribution

It provides a comprehensive formalism for these theories, including analysis of spherically symmetric matter, structure scalars, and minimal complexity models.

Findings

Maximum of three degrees of freedom in vacuum

Evaluation of structure scalars under Einstein's modifications

Proposal of minimal complexity and conformal flatness models

Abstract

We explore a comprehensive analysis of the formalism governing the gravitational field equations in degenerate higher-order scalar-tensor theories. The propagation of these theories in the vacuum has a maximum of three degrees of freedom and is at most quadratic in the second derivative of the scalar field. We investigate the gravitational field equation for spherically symmetric anisotropic matter content along with its non-conserved equations. Our analysis focuses on the evaluation of structure scalars to assess their behavior under Einstein's modification. We present a realistic mass contribution that sheds light on both geometric mass and total energy budget evaluations for celestial objects. Ultimately, we discuss two viable models restricted as minimal complexity and conformal flatness to enhance the scientific contribution of the present manuscript.