Brane worlds with bolts

TL;DR

This paper constructs a class of higher-dimensional brane world models with regular bulk boundaries called bolts, allowing for flexible low-energy spacetimes and analyzing gravitational behavior resembling scalar fields.

Contribution

It introduces a new family of brane world solutions with bolt boundaries, accommodating various Einstein spaces and analyzing gravitational potentials in these models.

Findings

Bulk solutions are regular at bolts, avoiding singularities.

The gravitational potential behaves like a massless scalar field with Neumann boundary conditions.

Long-distance potential matches p-dimensional behavior for Minkowski branes with zero bulk cosmological constant.

Abstract

We construct a family of (p+3)-dimensional brane worlds in which the brane has one compact extra dimension, the bulk has two extra dimensions, and the bulk closes regularly at codimension two submanifolds known as bolts. The (p+1)-dimensional low energy spacetime M_{low} may be any Einstein space with an arbitrary cosmological constant, the value of the bulk cosmological constant is arbitrary, and the only fields are the metric and a bulk Maxwell field. The brane can be chosen to have positive tension, and the closure of the bulk provides a singularity-free boundary condition for solutions that contain black holes or gravitational waves in M_{low}. The spacetimes admit a nonlinear gravitational wave whose properties suggest that the Newtonian gravitational potential on a flat M_{low} will behave essentially as the static potential of a massless minimally coupled scalar field with Neumann boundary conditions. When M_{low} is (p+1)-dimensional Minkowski with p\ge3 and the bulk cosmological constant vanishes, this static scalar potential is shown to have the long distance behaviour characteristic of p spatial dimensions.