Regularization of the linearized gravitational self-force for branes

TL;DR

This paper analyzes the gravitational self-force on branes of various codimensions, revealing that in certain cases the self-force vanishes, which has implications for brane-world models and the cosmological constant problem.

Contribution

It generalizes previous results on gravitational self-force to arbitrary codimension branes and identifies special properties of six-dimensional 3-brane models.

Findings

Self-force is zero for codimension two branes with Nambu-Goto equation of state.

Bare tension on the brane does not affect local physics.

Six-dimensional 3-brane models have unique properties related to self-force.

Abstract

We discuss the linearized, gravitational self-interaction of a brane of arbitrary codimension in a spacetime of arbitrary dimension. We find that in the codimension two case the gravitational self-force is exactly zero for a Nambu-Goto equation of state, generalizing a previous result for a string in four dimensions. For the case of a 3-brane, this picks out the case of a six-dimensional brane-world model as having special properties which we discuss. In particular, we see that bare tension on the brane has no effect locally, suppressing the cosmological constant problem.