Equation of motion for a domain wall coupled to gravitational field

TL;DR

This paper derives the equation of motion for a gravitationally coupled domain wall from the Nambu-Goto action, including perturbations and back reaction effects, expressed in gauge-invariant variables for spherically symmetric backgrounds.

Contribution

It presents a novel derivation of the domain wall's equation of motion considering gravitational coupling and perturbations, extending previous models.

Findings

Derived the fundamental equation of motion from the Nambu-Goto action.

Included gravitational back reaction in the perturbed equation.

Expressed the equations in gauge-invariant variables for spherical symmetry.

Abstract

The equation of motion for a domain wall coupled to gravitational field is derived from the Nambu-Goto action. The domain wall is treated as a source of gravitational field. The perturbed equation is also obtained with gravitational back reaction on the wall motion taken into account. For general spherically symmetric background case, the equation is expressed in terms of the gauge-invariant variables.