Gravitational trapping potential with arbitrary extra dimensions

TL;DR

This paper generalizes a non-singular 6D brane solution to higher dimensions, providing a gravitational trapping mechanism for various fields, with distinctions between 2 and more extra dimensions affecting the geometry and stress-energy properties.

Contribution

It introduces a new higher-dimensional brane solution with gravitational trapping capabilities, highlighting differences between two and more extra dimensions.

Findings

Provides a non-singular brane solution in higher dimensions.

Demonstrates gravitational trapping for multiple field spins.

Shows stress-energy tensor properties are physically reasonable.

Abstract

We extend a recently discovered, non-singular 6 dimensional brane, solution to D=4+n dimensions. As with the previous 6D solution the present solution provides a gravitational trapping mechanism for fields of spin 0, 1/2, 1 and 2. There is an important distinction between 2 extra dimensions and $n$ extra dimensions that makes this more than a trivial extension. In contrast to gravity in n >2 dimensions, gravity in n=2 dimensions is conformally flat. The stress-energy tensor required by this solution has reasonable physically properties, and for n=2 and n=3 can be made to asymptotically go to zero as one moves away from the brane.