Braneworld Gravity in Symmetric Space Bulk

TL;DR

This paper develops a geometric framework for braneworld gravity within symmetric space bulks, deriving Einstein equations based on the bulk geometry and brane dynamics, offering a novel approach to higher-dimensional gravity models.

Contribution

It introduces a method to express braneworld Einstein equations purely in terms of bulk coordinates using symmetric space geometry and the Gauss equation.

Findings

Derived bulk metric invariant under G in symmetric space gauge

Computed the Levi-Civita connection for the bulk metric

Presented a geometrical method for braneworld Einstein equations

Abstract

By considering the p-brane motion in G/K symmetric space bulk we identify the G-invariant bulk metric in the solvable lie algebra gauge of the brane action. After calculating the Levi-Civita connection of this bulk metric we use it in the Gauss equation to compute the braneworld curvature in terms of the bulk coordinates. Finally, by making use of the Gauss equation in the braneworld Einstein equation we present a geometrical method of implementing the first fundamental form in the gravitating brane dynamics for the specially chosen symmetric space bulk case leading to an Einstein equation solely expressed in terms of the bulk coordinates of the braneworld.