Bulk metric of brane world models and submanifolds in 6D pseudo-Euclidean space-time

TL;DR

This paper explores five-dimensional brane world models with de Sitter metrics, demonstrating their equivalence to submanifolds in six-dimensional pseudo-Euclidean space through explicit coordinate transformations, for both zero and non-zero bulk cosmological constants.

Contribution

It provides explicit coordinate transformations linking brane world bulk metrics to submanifolds in 6D pseudo-Euclidean space, clarifying their geometric structure.

Findings

Explicit transformations for zero cosmological constant

Explicit transformations for non-zero cosmological constant

Unified geometric interpretation of brane models

Abstract

In this short note, five-dimensional brane world models with dS_{4} metric on the branes are discussed. The explicit coordinate transformations, which show the equivalence between the bulk metric of these brane world models and the metric induced on an appropriate submanifolds in the flat six-dimensional pseudo-Euclidean space-time, are presented. The cases of the zero and non-zero cosmological constant in the bulk are discussed in detail.