3+1+1 dimensional covariant gravitational dynamics on an asymmetrically embedded brane

TL;DR

This paper derives evolution and constraint equations for a brane embedded asymmetrically in higher-dimensional spacetime, providing a covariant framework for gravitational dynamics in such models.

Contribution

It introduces a novel formulation of gravitational dynamics on an asymmetrically embedded brane using average and difference equations.

Findings

Derived evolution and constraint equations in covariant form

Presented a new approach for asymmetric brane embeddings

Facilitates analysis of gravitational behavior in higher-dimensional models

Abstract

We give the evolution and constraint equations on an asymmetrically embedded brane in the form of average and difference equations.